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Update app.py
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app.py
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import
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import json
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import re
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import random
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import time
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import
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from
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from
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#
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#
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question_verifier = None
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{
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"chapter": "1. Functions and Models",
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"subchapters": [
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"1.1 Four Ways to Represent a Function",
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"1.2 Mathematical Models",
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"1.3 New Functions from Old Functions",
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"1.4 Exponential Functions",
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"1.5 Inverse Functions and Logarithms",
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"1.6 Parametric Curves"
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],
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"key_formulas": [
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"Domain and Range",
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"Function composition: $(f \\circ g)(x) = f(g(x))$",
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"Exponential function: $f(x) = a^x$, where $a > 0$",
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"Natural exponential function: $f(x) = e^x$",
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"Logarithmic function: $f(x) = \\log_a(x)$, where $a > 0, a \\neq 1$",
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"Natural logarithm: $f(x) = \\ln(x)$"
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]
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},
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{
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"chapter": "2. Limits and Derivatives",
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"subchapters": [
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"2.1 The Tangent and Velocity Problems",
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"2.2 The Limit of a Function",
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"2.3 Calculating Limits",
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"2.4 Continuity",
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"2.5 The Derivative",
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"2.6 The Derivative as a Function",
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"2.7 Derivatives of Trigonometric Functions",
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"2.8 The Chain Rule",
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"2.9 Implicit Differentiation",
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"2.10 Related Rates",
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"2.11 Linear Approximations and Differentials"
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],
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"key_formulas": [
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"Limit Definition: $\\lim_{x \\to a} f(x) = L$",
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"Derivative Definition: $f'(x) = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h}$",
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"Power Rule: $\\frac{d}{dx}(x^n) = nx^{n-1}$",
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"Product Rule: $\\frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)$",
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"Quotient Rule: $\\frac{d}{dx}\\left[\\frac{f(x)}{g(x)}\\right] = \\frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$",
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"Chain Rule: $\\frac{d}{dx}[f(g(x))] = f'(g(x)) \\cdot g'(x)$"
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]
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},
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{
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"chapter": "3. Applications of Differentiation",
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"subchapters": [
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"3.1 Maximum and Minimum Values",
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"3.2 The Mean Value Theorem",
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"3.3 How Derivatives Affect the Shape of a Graph",
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"3.4 Indeterminate Forms and L'Hospital's Rule",
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"3.5 Summary of Curve Sketching",
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"3.6 Optimization Problems",
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"3.7 Newton's Method",
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"3.8 Antiderivatives"
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],
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"key_formulas": [
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"Critical Points: $f'(x) = 0$ or $f'(x)$ is undefined",
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"Mean Value Theorem: If $f$ is continuous on $[a, b]$ and differentiable on $(a, b)$, then there exists a $c$ in $(a, b)$ such that $f'(c) = \\frac{f(b) - f(a)}{b - a}$",
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"Second Derivative Test: If $f'(c) = 0$ and $f''(c) > 0$, then $f$ has a local minimum at $c$",
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"L'Hospital's Rule: $\\lim_{x \\to a}\\frac{f(x)}{g(x)} = \\lim_{x \\to a}\\frac{f'(x)}{g'(x)}$",
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"Newton's Method: $x_{n+1} = x_n - \\frac{f(x_n)}{f'(x_n)}$"
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]
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},
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{
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"chapter": "4. Integrals",
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"subchapters": [
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"4.1 Areas and Distances",
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"4.2 The Definite Integral",
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"4.3 The Fundamental Theorem of Calculus",
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"4.4 Indefinite Integrals and the Net Change Theorem",
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"4.5 The Substitution Rule"
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],
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"key_formulas": [
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"Definite Integral: $\\int_a^b f(x)\\,dx = \\lim_{n \\to \\infty} \\sum_{i=1}^{n} f(x_i^*)\\Delta x$",
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"Fundamental Theorem of Calculus: $\\int_a^b f(x)\\,dx = F(b) - F(a)$ where $F'(x) = f(x)$",
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"Indefinite Integral: $\\int f(x)\\,dx = F(x) + C$ where $F'(x) = f(x)$",
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"Power Rule for Integration: $\\int x^n\\,dx = \\frac{x^{n+1}}{n+1} + C$ for $n \\neq -1$",
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"Substitution Rule: $\\int f(g(x))g'(x)\\,dx = \\int f(u)\\,du$ where $u = g(x)$"
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]
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},
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{
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"chapter": "5. Applications of Integration",
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"subchapters": [
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"5.1 Areas Between Curves",
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"5.2 Volumes",
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"5.3 Volumes by Cylindrical Shells",
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"5.4 Work",
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"5.5 Average Value of a Function"
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],
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"key_formulas": [
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"Area Between Curves: $\\int_a^b [f(x) - g(x)]\\,dx$ where $f(x) \\geq g(x)$",
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"Volume by Disk Method: $V = \\pi\\int_a^b [R(x)]^2\\,dx$",
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"Volume by Washer Method: $V = \\pi\\int_a^b [(R(x))^2 - (r(x))^2]\\,dx$",
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"Volume by Cylindrical Shells: $V = 2\\pi\\int_a^b xf(x)\\,dx$ for rotation about y-axis",
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"Average Value of $f$ on $[a,b]$: $f_{avg} = \\frac{1}{b-a}\\int_a^b f(x)\\,dx$",
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"Work: $W = \\int_a^b F(x)\\,dx$"
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]
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},
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{
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"chapter": "6. Techniques of Integration",
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"subchapters": [
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"6.1 Integration by Parts",
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"6.2 Trigonometric Integrals",
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"6.3 Trigonometric Substitution",
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"6.4 Integration of Rational Functions by Partial Fractions",
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"6.5 Strategy for Integration",
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"6.6 Approximate Integration",
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"6.7 Improper Integrals"
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],
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"key_formulas": [
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"Integration by Parts: $\\int u\\,dv = uv - \\int v\\,du$",
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"Trigonometric Integrals: $\\int \\sin^n x \\cos^m x\\,dx$ (various formulas)",
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"Trig Substitution: $x = a\\sin\\theta$ for $\\sqrt{a^2-x^2}$, $x = a\\tan\\theta$ for $\\sqrt{a^2+x^2}$",
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"Partial Fractions: $\\frac{P(x)}{Q(x)} = \\frac{A}{(x-a)} + \\frac{B}{(x-a)^2} + \\frac{Cx+D}{x^2+bx+c} + ...$",
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"Improper Integrals: $\\int_a^{\\infty} f(x)\\,dx = \\lim_{t \\to \\infty} \\int_a^t f(x)\\,dx$"
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]
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},
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{
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"chapter": "7. Differential Equations",
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"subchapters": [
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"7.1 Modeling with Differential Equations",
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"7.2 Direction Fields and Euler's Method",
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"7.3 Separable Equations",
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"7.4 Models for Population Growth",
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"7.5 Linear Equations",
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"7.6 Predator-Prey Systems"
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],
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"key_formulas": [
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"General form of a first-order differential equation: $\\frac{dy}{dx} = f(x, y)$",
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"Separable equation: $\\frac{dy}{dx} = g(x)h(y)$ → $\\int \\frac{1}{h(y)}dy = \\int g(x)dx + C$",
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"First-order linear differential equation: $\\frac{dy}{dx} + P(x)y = Q(x)$",
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"Integrating factor method: Multiply by $e^{\\int P(x)dx}$",
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"Euler's Method: $y_{n+1} = y_n + hf(x_n, y_n)$"
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]
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},
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{
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"chapter": "8. Infinite Sequences and Series",
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"subchapters": [
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"8.1 Sequences",
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"8.2 Series",
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"8.3 The Integral Test and Estimates of Sums",
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"8.4 The Comparison Tests",
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"8.5 Alternating Series",
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"8.6 Absolute Convergence and the Ratio and Root Tests",
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"8.7 Strategy for Testing Series",
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"8.8 Power Series",
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"8.9 Representations of Functions as Power Series",
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"8.10 Taylor and Maclaurin Series"
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],
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"key_formulas": [
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"Geometric Series: $\\sum_{n=0}^{\\infty} ar^n = \\frac{a}{1-r}$ if $|r| < 1$",
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"Taylor Series: $f(x) = \\sum_{n=0}^{\\infty} \\frac{f^{(n)}(a)}{n!}(x-a)^n$",
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"Maclaurin Series: $f(x) = \\sum_{n=0}^{\\infty} \\frac{f^{(n)}(0)}{n!}x^n$",
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"Common Maclaurin Series: $e^x = \\sum_{n=0}^{\\infty} \\frac{x^n}{n!}$, $\\sin(x) = \\sum_{n=0}^{\\infty} \\frac{(-1)^n}{(2n+1)!}x^{2n+1}$",
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"Ratio Test: $\\lim_{n \\to \\infty} |\\frac{a_{n+1}}{a_n}| < 1$ implies convergence"
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]
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},
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{
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"chapter": "9. Parametric Equations and Polar Coordinates",
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"subchapters": [
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"9.1 Parametric Curves",
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"9.2 Calculus with Parametric Curves",
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"9.3 Polar Coordinates",
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"9.4 Areas and Lengths in Polar Coordinates",
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"9.5 Conic Sections"
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],
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"key_formulas": [
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"Parametric curve: $x = f(t)$, $y = g(t)$",
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"Arc length of parametric curve: $L = \\int_a^b \\sqrt{[f'(t)]^2 + [g'(t)]^2}\\,dt$",
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"Polar to rectangular coordinates: $x = r\\cos\\theta$, $y = r\\sin\\theta$",
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"Rectangular to polar coordinates: $r = \\sqrt{x^2 + y^2}$, $\\theta = \\arctan(\\frac{y}{x})$",
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"Area in polar coordinates: $A = \\frac{1}{2}\\int_{\\alpha}^{\\beta} [r(\\theta)]^2\\,d\\theta$"
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]
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},
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{
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"chapter": "10. Vectors and the Geometry of Space",
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"subchapters": [
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"10.1 Three-Dimensional Coordinate Systems",
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"10.2 Vectors",
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"10.3 The Dot Product",
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"10.4 The Cross Product",
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"10.5 Equations of Lines and Planes",
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"10.6 Cylinders and Quadric Surfaces"
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],
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"key_formulas": [
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"Dot Product: $\\vec{a} \\cdot \\vec{b} = |\\vec{a}||\\vec{b}|\\cos\\theta$",
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"Cross Product: $\\vec{a} \\times \\vec{b} = |\\vec{a}||\\vec{b}|\\sin\\theta\\,\\vec{n}$",
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"Equation of a line: $\\vec{r} = \\vec{r_0} + t\\vec{v}$",
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"Equation of a plane: $\\vec{n} \\cdot (\\vec{r} - \\vec{r_0}) = 0$ or $ax + by + cz + d = 0$",
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"Distance from point to plane: $d = \\frac{|ax_0 + by_0 + cz_0 + d|}{\\sqrt{a^2 + b^2 + c^2}}$"
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]
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},
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{
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"chapter": "11. Vector Functions",
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"subchapters": [
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"11.1 Vector Functions and Space Curves",
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"11.2 Derivatives and Integrals of Vector Functions",
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"11.3 Arc Length and Curvature",
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"11.4 Motion in Space: Velocity and Acceleration"
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],
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"key_formulas": [
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"Vector function: $\\vec{r}(t) = x(t)\\vec{i} + y(t)\\vec{j} + z(t)\\vec{k}$",
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"Derivative of vector function: $\\vec{r}'(t) = x'(t)\\vec{i} + y'(t)\\vec{j} + z'(t)\\vec{k}$",
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"Arc length: $L = \\int_a^b |\\vec{r}'(t)|\\,dt$",
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"Unit tangent vector: $\\vec{T}(t) = \\frac{\\vec{r}'(t)}{|\\vec{r}'(t)|}$",
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"Curvature: $\\kappa = \\frac{|\\vec{T}'(t)|}{|\\vec{r}'(t)|}$",
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"Acceleration: $\\vec{a}(t) = \\vec{r}''(t)$"
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]
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},
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{
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"chapter": "12. Partial Derivatives",
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"subchapters": [
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"12.1 Functions of Several Variables",
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"12.2 Limits and Continuity",
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"12.3 Partial Derivatives",
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"12.4 Tangent Planes and Linear Approximations",
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"12.5 The Chain Rule",
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"12.6 Directional Derivatives and the Gradient Vector",
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"12.7 Maximum and Minimum Values",
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"12.8 Lagrange Multipliers"
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],
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"key_formulas": [
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"Partial derivative: $\\frac{\\partial f}{\\partial x}(x_0, y_0)$",
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"Gradient: $\\nabla f = \\frac{\\partial f}{\\partial x}\\vec{i} + \\frac{\\partial f}{\\partial y}\\vec{j} + \\frac{\\partial f}{\\partial z}\\vec{k}$",
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"Directional derivative: $D_\\vec{u}f = \\nabla f \\cdot \\vec{u}$",
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"Tangent plane: $z - z_0 = f_x(x_0, y_0)(x - x_0) + f_y(x_0, y_0)(y - y_0)$",
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"Chain Rule: $\\frac{dz}{dt} = \\frac{\\partial z}{\\partial x}\\frac{dx}{dt} + \\frac{\\partial z}{\\partial y}\\frac{dy}{dt}$"
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]
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},
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{
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"chapter": "13. Multiple Integrals",
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"subchapters": [
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"13.1 Double Integrals over Rectangles",
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"13.2 Iterated Integrals",
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"13.3 Double Integrals over General Regions",
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"13.4 Double Integrals in Polar Coordinates",
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"13.5 Applications of Double Integrals",
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"13.6 Triple Integrals",
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"13.7 Triple Integrals in Cylindrical Coordinates",
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"13.8 Triple Integrals in Spherical Coordinates",
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"13.9 Change of Variables in Multiple Integrals"
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],
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"key_formulas": [
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"Double integral: $\\iint_R f(x,y)\\,dA = \\int_a^b \\int_c^d f(x,y)\\,dy\\,dx$",
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"Area in polar coordinates: $\\iint_R f(r,\\theta)\\,dA = \\int_{\\alpha}^{\\beta} \\int_{h_1(\\theta)}^{h_2(\\theta)} f(r,\\theta)\\,r\\,dr\\,d\\theta$",
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"Triple integral: $\\iiint_E f(x,y,z)\\,dV$",
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"Cylindrical coordinates: $\\iiint_E f(x,y,z)\\,dV = \\iiint_E f(r\\cos\\theta, r\\sin\\theta, z)\\,r\\,dr\\,d\\theta\\,dz$",
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"Spherical coordinates: $\\iiint_E f(x,y,z)\\,dV = \\iiint_E f(\\rho\\sin\\phi\\cos\\theta, \\rho\\sin\\phi\\sin\\theta, \\rho\\cos\\phi)\\,\\rho^2\\sin\\phi\\,d\\rho\\,d\\phi\\,d\\theta$"
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]
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},
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{
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"chapter": "14. Vector Calculus",
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"subchapters": [
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"14.1 Vector Fields",
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"14.2 Line Integrals",
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"14.3 The Fundamental Theorem for Line Integrals",
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"14.4 Green's Theorem",
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"14.5 Curl and Divergence",
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"14.6 Surface Integrals",
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"14.7 Stokes' Theorem",
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"14.8 The Divergence Theorem"
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],
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"key_formulas": [
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"Line integral of scalar function: $\\int_C f(x,y,z)\\,ds = \\int_a^b f(\\vec{r}(t))|\\vec{r}'(t)|\\,dt$",
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"Line integral of vector field: $\\int_C \\vec{F} \\cdot d\\vec{r} = \\int_a^b \\vec{F}(\\vec{r}(t)) \\cdot \\vec{r}'(t)\\,dt$",
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"Green's Theorem: $\\oint_C (P\\,dx + Q\\,dy) = \\iint_D (\\frac{\\partial Q}{\\partial x} - \\frac{\\partial P}{\\partial y})\\,dA$",
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"Divergence: $\\text{div}\\,\\vec{F} = \\nabla \\cdot \\vec{F} = \\frac{\\partial P}{\\partial x} + \\frac{\\partial Q}{\\partial y} + \\frac{\\partial R}{\\partial z}$",
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"Curl: $\\text{curl}\\,\\vec{F} = \\nabla \\times \\vec{F}$",
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"Stokes' Theorem: $\\int_S (\\nabla \\times \\vec{F}) \\cdot d\\vec{S} = \\oint_C \\vec{F} \\cdot d\\vec{r}$",
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"Divergence Theorem: $\\iiint_E (\\nabla \\cdot \\vec{F})\\,dV = \\iint_{\\partial E} \\vec{F} \\cdot d\\vec{S}$"
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]
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}
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]
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def load_models_if_needed():
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"""Ensures models are loaded when needed"""
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global question_generator, question_verifier
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"""
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if chapter_idx < 0 or chapter_idx >= len(calculus_curriculum):
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return "Invalid chapter selection."
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chapter = calculus_curriculum[chapter_idx]
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return
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prompt = f"""Create {num_questions} university-level mathematics questions about {subchapter} from {chapter} at {difficulty} difficulty.
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For each question:
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1. Write a clear, university-level calculus problem
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2.
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3.
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Format your response exactly as follows:
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[
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Step
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Step 2: [Second step]
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...
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### Answer
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[Final answer]
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## Question 2
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...
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Make sure
|
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"""
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return prompt
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def verify_question(question_text, solution_text):
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"""Verify if the question and solution are mathematically sound"""
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error_msg = load_models_if_needed()
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if error_msg:
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return False, error_msg
|
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verification_prompt = f"""Verify if this calculus question and solution are mathematically correct:
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Question: {question_text}
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#
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return True, "Verification passed"
|
393 |
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else:
|
394 |
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# Extract the explanation for why it's incorrect
|
395 |
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explanation = verification.split("No")[1] if "No" in verification else "Unable to determine specific issue"
|
396 |
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return False, f"Verification failed: {explanation}"
|
397 |
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except Exception as e:
|
398 |
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return False, f"Error during verification: {str(e)}"
|
399 |
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|
400 |
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def generate_questions(chapter_index, subchapter_index, difficulty, num_questions):
|
401 |
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"""Generate mathematics questions based on chapter/subchapter"""
|
402 |
-
error_msg = load_models_if_needed()
|
403 |
-
if error_msg:
|
404 |
-
return f"## Error Loading Models\n\n{error_msg}\n\nPlease try again later or contact the administrator."
|
405 |
-
|
406 |
-
# Get chapter and subchapter information
|
407 |
-
if chapter_index < 0 or chapter_index >= len(calculus_curriculum):
|
408 |
-
return "Please select a valid chapter."
|
409 |
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419 |
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420 |
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421 |
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422 |
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|
423 |
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temperature=0.7, top_p=0.85, num_return_sequences=1)[0]['generated_text']
|
424 |
|
425 |
-
#
|
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427 |
|
428 |
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#
|
429 |
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430 |
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431 |
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|
432 |
|
433 |
-
#
|
434 |
-
|
435 |
-
|
436 |
-
result = generate_fallback_questions(chapter["chapter"], subchapter, num_questions)
|
437 |
|
438 |
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|
439 |
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|
440 |
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442 |
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443 |
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444 |
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|
445 |
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|
446 |
-
|
447 |
-
def generate_fallback_questions(chapter, subchapter, num_questions):
|
448 |
-
"""Generate fallback questions when model generation fails"""
|
449 |
-
# Basic templates for different calculus topics
|
450 |
-
if "Limits" in chapter or "Limits" in subchapter:
|
451 |
-
questions = [
|
452 |
-
{
|
453 |
-
"question": "Evaluate the limit: $\\lim_{x \\to 2} \\frac{x^3 - 8}{x - 2}$",
|
454 |
-
"solution": "Step 1: Note that this is an indeterminate form (0/0) when x = 2.\n" +
|
455 |
-
"Step 2: Factor the numerator: $x^3 - 8 = (x - 2)(x^2 + 2x + 4)$\n" +
|
456 |
-
"Step 3: Simplify: $\\lim_{x \\to 2} \\frac{(x - 2)(x^2 + 2x + 4)}{x - 2} = \\lim_{x \\to 2} (x^2 + 2x + 4)$\n" +
|
457 |
-
"Step 4: Evaluate by direct substitution: $2^2 + 2(2) + 4 = 4 + 4 + 4 = 12$",
|
458 |
-
"answer": "12"
|
459 |
-
},
|
460 |
-
{
|
461 |
-
"question": "Find the limit: $\\lim_{x \\to 0} \\frac{\\sin(3x)}{x}$",
|
462 |
-
"solution": "Step 1: Rewrite using the limit property $\\lim_{x \\to 0} \\frac{\\sin x}{x} = 1$\n" +
|
463 |
-
"Step 2: $\\lim_{x \\to 0} \\frac{\\sin(3x)}{x} = \\lim_{x \\to 0} 3 \\cdot \\frac{\\sin(3x)}{3x}$\n" +
|
464 |
-
"Step 3: Apply the limit property: $3 \\cdot \\lim_{x \\to 0} \\frac{\\sin(3x)}{3x} = 3 \\cdot 1 = 3$",
|
465 |
-
"answer": "3"
|
466 |
-
}
|
467 |
-
]
|
468 |
-
elif "Derivative" in chapter or "Derivative" in subchapter:
|
469 |
-
questions = [
|
470 |
-
{
|
471 |
-
"question": "Find the derivative of $f(x) = x^3\\ln(x) - \\frac{x^3}{3}$",
|
472 |
-
"solution": "Step 1: Use the product rule on $x^3\\ln(x)$\n" +
|
473 |
-
"$\\frac{d}{dx}[x^3\\ln(x)] = x^3 \\cdot \\frac{1}{x} + \\ln(x) \\cdot 3x^2$\n" +
|
474 |
-
"$= x^2 + 3x^2\\ln(x)$\n" +
|
475 |
-
"Step 2: Find the derivative of $\\frac{x^3}{3}$\n" +
|
476 |
-
"$\\frac{d}{dx}[\\frac{x^3}{3}] = \\frac{3x^2}{3} = x^2$\n" +
|
477 |
-
"Step 3: Combine the results\n" +
|
478 |
-
"$f'(x) = x^2 + 3x^2\\ln(x) - x^2 = 3x^2\\ln(x)$",
|
479 |
-
"answer": "$f'(x) = 3x^2\\ln(x)$"
|
480 |
-
}
|
481 |
-
]
|
482 |
-
elif "Integration" in chapter or "Integral" in chapter or "Integration" in subchapter or "Integral" in subchapter:
|
483 |
-
questions = [
|
484 |
-
{
|
485 |
-
"question": "Evaluate the integral: $\\int x^2\\ln(x) dx$",
|
486 |
-
"solution": "Step 1: Use integration by parts with $u = \\ln(x)$ and $dv = x^2 dx$\n" +
|
487 |
-
"Then $du = \\frac{1}{x}dx$ and $v = \\frac{x^3}{3}$\n" +
|
488 |
-
"Step 2: Apply the formula $\\int u dv = uv - \\int v du$\n" +
|
489 |
-
"$\\int x^2\\ln(x) dx = \\ln(x) \\cdot \\frac{x^3}{3} - \\int \\frac{x^3}{3} \\cdot \\frac{1}{x} dx$\n" +
|
490 |
-
"$= \\frac{x^3\\ln(x)}{3} - \\frac{1}{3}\\int x^2 dx$\n" +
|
491 |
-
"$= \\frac{x^3\\ln(x)}{3} - \\frac{1}{3} \\cdot \\frac{x^3}{3} + C$\n" +
|
492 |
-
"$= \\frac{x^3\\ln(x)}{3} - \\frac{x^3}{9} + C$",
|
493 |
-
"answer": "$\\frac{x^3\\ln(x)}{3} - \\frac{x^3}{9} + C$"
|
494 |
-
}
|
495 |
-
]
|
496 |
-
else:
|
497 |
-
# Generic calculus questions
|
498 |
-
questions = [
|
499 |
-
{
|
500 |
-
"question": "Find the critical points of $f(x) = x^3 - 6x^2 + 12x + 5$ and determine their nature.",
|
501 |
-
"solution": "Step 1: Find the derivative: $f'(x) = 3x^2 - 12x + 12$\n" +
|
502 |
-
"Step 2: Set $f'(x) = 0$ and solve: $3x^2 - 12x + 12 = 0$\n" +
|
503 |
-
"Step 3: Simplify: $x^2 - 4x + 4 = 0$\n" +
|
504 |
-
"Step 4: Factor: $(x - 2)^2 = 0$\n" +
|
505 |
-
"Step 5: Therefore $x = 2$ is a critical point (with multiplicity 2)\n" +
|
506 |
-
"Step 6: Find the second derivative: $f''(x) = 6x - 12$\n" +
|
507 |
-
"Step 7: Evaluate at $x = 2$: $f''(2) = 6(2) - 12 = 0$\n" +
|
508 |
-
"Step 8: Since $f''(2) = 0$, the second derivative test is inconclusive\n" +
|
509 |
-
"Step 9: Checking $f'(x)$ around $x = 2$:\n" +
|
510 |
-
"For $x < 2$, $f'(x) < 0$ and for $x > 2$, $f'(x) > 0$\n" +
|
511 |
-
"Step 10: Therefore, $x = 2$ is a point of inflection",
|
512 |
-
"answer": "$x = 2$ is a critical point and an inflection point"
|
513 |
-
}
|
514 |
-
]
|
515 |
-
|
516 |
-
# Get a random subset of questions or duplicate if we need more
|
517 |
-
result_questions = []
|
518 |
-
for i in range(num_questions):
|
519 |
-
idx = i % len(questions)
|
520 |
-
q = questions[idx]
|
521 |
-
result_questions.append({
|
522 |
-
"id": i+1,
|
523 |
-
"question": q["question"],
|
524 |
-
"solution": q["solution"],
|
525 |
-
"answer": q["answer"]
|
526 |
-
})
|
527 |
-
|
528 |
-
# Format the output
|
529 |
-
result = ""
|
530 |
-
for q in result_questions:
|
531 |
-
result += f"## Question {q['id']}\n{q['question']}\n\n"
|
532 |
-
result += f"### Solution\n{q['solution']}\n\n"
|
533 |
-
result += f"### Answer\n{q['answer']}\n\n"
|
534 |
-
|
535 |
-
return result
|
536 |
-
|
537 |
-
def on_chapter_change(chapter_index):
|
538 |
-
"""Update subchapter dropdown based on selected chapter"""
|
539 |
-
if chapter_index < 0 or chapter_index >= len(calculus_curriculum):
|
540 |
-
return gr.Dropdown(choices=[], value=None)
|
541 |
-
|
542 |
-
subchapters = calculus_curriculum[chapter_index]["subchapters"]
|
543 |
-
return gr.Dropdown(choices=subchapters, value=subchapters[0] if subchapters else None)
|
544 |
|
545 |
-
def
|
546 |
-
|
547 |
-
|
548 |
-
chapters = [chapter["chapter"] for chapter in calculus_curriculum]
|
549 |
|
550 |
-
|
551 |
-
|
552 |
-
gr.Markdown("Generate university-level calculus questions with step-by-step solutions.")
|
553 |
-
|
554 |
-
with gr.Row():
|
555 |
-
with gr.Column(scale=2):
|
556 |
-
chapter_dropdown = gr.Dropdown(
|
557 |
-
choices=chapters,
|
558 |
-
value=chapters[0] if chapters else None,
|
559 |
-
label="Chapter",
|
560 |
-
info="Select a chapter from Stewart's Calculus"
|
561 |
-
)
|
562 |
-
|
563 |
-
subchapter_dropdown = gr.Dropdown(
|
564 |
-
choices=calculus_curriculum[0]["subchapters"] if calculus_curriculum else [],
|
565 |
-
value=calculus_curriculum[0]["subchapters"][0] if calculus_curriculum and calculus_curriculum[0]["subchapters"] else None,
|
566 |
-
label="Subchapter",
|
567 |
-
info="Select a specific subchapter"
|
568 |
-
)
|
569 |
-
|
570 |
-
with gr.Row():
|
571 |
-
num_questions = gr.Slider(
|
572 |
-
minimum=1,
|
573 |
-
maximum=5,
|
574 |
-
value=DEFAULT_NUM_QUESTIONS,
|
575 |
-
step=1,
|
576 |
-
label="Number of Questions"
|
577 |
-
)
|
578 |
-
|
579 |
-
difficulty = gr.Dropdown(
|
580 |
-
choices=["Easy", "Medium", "Hard", "Advanced"],
|
581 |
-
value=DEFAULT_DIFFICULTY,
|
582 |
-
label="Difficulty Level"
|
583 |
-
)
|
584 |
-
|
585 |
-
generate_button = gr.Button("Generate Questions", variant="primary")
|
586 |
-
|
587 |
-
output = gr.Markdown(label="Generated Questions & Solutions")
|
588 |
-
|
589 |
-
# Handle chapter selection change
|
590 |
-
chapter_dropdown.change(
|
591 |
-
fn=on_chapter_change,
|
592 |
-
inputs=[chapter_dropdown],
|
593 |
-
outputs=[subchapter_dropdown]
|
594 |
-
)
|
595 |
-
|
596 |
-
# Handle generate button click
|
597 |
-
generate_button.click(
|
598 |
-
fn=generate_questions,
|
599 |
-
inputs=[
|
600 |
-
gr.State(lambda: chapters.index(chapter_dropdown.value) if chapter_dropdown.value in chapters else 0),
|
601 |
-
gr.State(lambda: calculus_curriculum[chapters.index(chapter_dropdown.value) if chapter_dropdown.value in chapters else 0]["subchapters"].index(subchapter_dropdown.value) if subchapter_dropdown.value in calculus_curriculum[chapters.index(chapter_dropdown.value) if chapter_dropdown.value in chapters else 0]["subchapters"] else 0),
|
602 |
-
difficulty,
|
603 |
-
num_questions
|
604 |
-
],
|
605 |
-
outputs=[output]
|
606 |
-
)
|
607 |
-
|
608 |
-
gr.Markdown("---")
|
609 |
-
gr.Markdown("Created by Kamagelo Mosia | Based on James Stewart's Calculus curriculum")
|
610 |
|
611 |
-
|
|
|
|
|
|
|
612 |
|
613 |
-
|
614 |
-
|
615 |
-
demo.launch()
|
|
|
1 |
+
import os
|
2 |
+
import torch
|
3 |
import json
|
|
|
|
|
4 |
import time
|
5 |
+
import logging
|
6 |
+
from datetime import datetime
|
7 |
+
from threading import Thread
|
8 |
+
from queue import Queue
|
9 |
+
from transformers import AutoTokenizer, AutoModelForCausalLM
|
10 |
|
11 |
+
# Configuration
|
12 |
+
PRIMARY_MODEL = "TinyLlama/TinyLlama-1.1B-Chat-v1.0" # First model to try
|
13 |
+
SECONDARY_MODEL = "facebook/opt-1.3b" # More powerful backup model
|
14 |
+
DEVICE = "cuda" if torch.cuda.is_available() else "cpu"
|
15 |
+
BATCH_SIZE = 5 # Process 5 chapters at a time
|
16 |
+
MAX_RETRIES = 3
|
17 |
+
OUTPUT_DIR = "calculus_textbook_output"
|
18 |
+
LOG_FILE = "textbook_generation.log"
|
19 |
|
20 |
+
# Setup logging
|
21 |
+
os.makedirs(OUTPUT_DIR, exist_ok=True)
|
22 |
+
logging.basicConfig(
|
23 |
+
filename=os.path.join(OUTPUT_DIR, LOG_FILE),
|
24 |
+
level=logging.INFO,
|
25 |
+
format='%(asctime)s - %(levelname)s - %(message)s'
|
26 |
+
)
|
|
|
27 |
|
28 |
+
class ModelManager:
|
29 |
+
"""Manages loading and switching between language models for text generation."""
|
|
|
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30 |
|
31 |
+
def __init__(self):
|
32 |
+
self.models = {}
|
33 |
+
self.tokenizers = {}
|
34 |
+
self.current_model = None
|
35 |
+
|
36 |
+
def load_model(self, model_name):
|
37 |
+
"""Load a model and its tokenizer if not already loaded."""
|
38 |
+
if model_name not in self.models:
|
39 |
+
try:
|
40 |
+
logging.info(f"Loading model: {model_name}")
|
41 |
+
tokenizer = AutoTokenizer.from_pretrained(model_name)
|
42 |
+
model = AutoModelForCausalLM.from_pretrained(
|
43 |
+
model_name,
|
44 |
+
torch_dtype=torch.float16 if DEVICE == "cuda" else torch.float32,
|
45 |
+
device_map="auto" if DEVICE == "cuda" else None
|
46 |
+
)
|
47 |
+
model.eval()
|
48 |
+
|
49 |
+
self.models[model_name] = model
|
50 |
+
self.tokenizers[model_name] = tokenizer
|
51 |
+
logging.info(f"Successfully loaded model: {model_name}")
|
52 |
+
return True
|
53 |
+
except Exception as e:
|
54 |
+
logging.error(f"Failed to load model {model_name}: {str(e)}")
|
55 |
+
return False
|
56 |
+
return True
|
57 |
|
58 |
+
def set_current_model(self, model_name):
|
59 |
+
"""Set the current model to use for generation."""
|
60 |
+
if model_name not in self.models and not self.load_model(model_name):
|
61 |
+
return False
|
62 |
+
self.current_model = model_name
|
63 |
+
return True
|
64 |
|
65 |
+
def generate_text(self, prompt, max_length=1024):
|
66 |
+
"""Generate text using the current model."""
|
67 |
+
if not self.current_model:
|
68 |
+
raise ValueError("No model selected. Call set_current_model first.")
|
69 |
+
|
70 |
+
model = self.models[self.current_model]
|
71 |
+
tokenizer = self.tokenizers[self.current_model]
|
72 |
+
|
73 |
+
inputs = tokenizer(prompt, return_tensors="pt").to(model.device)
|
74 |
+
|
75 |
+
# Generate with some randomness for creativity
|
76 |
+
with torch.no_grad():
|
77 |
+
outputs = model.generate(
|
78 |
+
**inputs,
|
79 |
+
max_length=max_length,
|
80 |
+
temperature=0.7,
|
81 |
+
top_p=0.9,
|
82 |
+
do_sample=True,
|
83 |
+
pad_token_id=tokenizer.eos_token_id
|
84 |
+
)
|
85 |
+
|
86 |
+
response = tokenizer.decode(outputs[0], skip_special_tokens=True)
|
87 |
+
# Extract only the generated part
|
88 |
+
generated_text = response[len(tokenizer.decode(inputs['input_ids'][0], skip_special_tokens=True)):].strip()
|
89 |
+
return generated_text
|
90 |
|
91 |
+
class CalculusTextbookGenerator:
|
92 |
+
"""Generates a complete calculus textbook with questions and solutions."""
|
|
|
|
|
|
|
|
|
93 |
|
94 |
+
def __init__(self):
|
95 |
+
self.model_manager = ModelManager()
|
96 |
+
self.textbook_data = self.create_initial_textbook_structure()
|
97 |
+
|
98 |
+
def create_initial_textbook_structure(self):
|
99 |
+
"""Create the initial structure of the calculus textbook."""
|
100 |
+
return {
|
101 |
+
"books": [
|
102 |
+
{
|
103 |
+
"name": "Calculus 1: Early Transcendentals",
|
104 |
+
"details": "Introduction to single-variable calculus including limits, derivatives, and basic integration techniques.",
|
105 |
+
"chapters": [
|
106 |
+
{
|
107 |
+
"chapterTitle": "Chapter 6: Applications of Integration",
|
108 |
+
"subChapters": [
|
109 |
+
"6.1: Areas Between Curves",
|
110 |
+
"6.2: Volumes",
|
111 |
+
"6.3: Volumes by Cylindrical Shells",
|
112 |
+
"6.4: Work",
|
113 |
+
"6.5: Average Value of a Function"
|
114 |
+
],
|
115 |
+
"questions": [] # Will be filled with generated questions
|
116 |
+
},
|
117 |
+
{
|
118 |
+
"chapterTitle": "Chapter 8: Further Applications of Integration",
|
119 |
+
"subChapters": [
|
120 |
+
"8.1: Arc Length",
|
121 |
+
"8.2: Area of a Surface of Revolution",
|
122 |
+
"8.3: Applications to Physics and Engineering",
|
123 |
+
"8.4: Applications to Economics and Biology",
|
124 |
+
"8.5: Probability"
|
125 |
+
],
|
126 |
+
"questions": []
|
127 |
+
},
|
128 |
+
{
|
129 |
+
"chapterTitle": "Chapter 9: Differential Equations",
|
130 |
+
"subChapters": [
|
131 |
+
"9.1: Modeling with Differential Equations",
|
132 |
+
"9.2: Direction Fields and Euler's Method",
|
133 |
+
"9.3: Separable Equations",
|
134 |
+
"9.4: Models for Population Growth",
|
135 |
+
"9.5: Linear Equations",
|
136 |
+
"9.6: Predator–Prey Systems"
|
137 |
+
],
|
138 |
+
"questions": []
|
139 |
+
},
|
140 |
+
{
|
141 |
+
"chapterTitle": "Chapter 10: Parametric Equations and Polar Coordinates",
|
142 |
+
"subChapters": [
|
143 |
+
"10.1: Curves Defined by Parametric Equations",
|
144 |
+
"10.2: Calculus with Parametric Curves",
|
145 |
+
"10.3: Polar Coordinates",
|
146 |
+
"10.4: Calculus in Polar Coordinates",
|
147 |
+
"10.5: Conic Sections",
|
148 |
+
"10.6: Conic Sections in Polar Coordinates"
|
149 |
+
],
|
150 |
+
"questions": []
|
151 |
+
},
|
152 |
+
{
|
153 |
+
"chapterTitle": "Chapter 11: Sequences, Series, and Power Series",
|
154 |
+
"subChapters": [
|
155 |
+
"11.1: Sequences",
|
156 |
+
"11.2: Series",
|
157 |
+
"11.3: The Integral Test and Estimates of Sums",
|
158 |
+
"11.4: The Comparison Tests",
|
159 |
+
"11.5: Alternating Series and Absolute Convergence",
|
160 |
+
"11.6: The Ratio and Root Tests",
|
161 |
+
"11.7: Power Series"
|
162 |
+
],
|
163 |
+
"questions": []
|
164 |
+
}
|
165 |
+
]
|
166 |
+
},
|
167 |
+
{
|
168 |
+
"name": "Calculus 2: Advanced Concepts",
|
169 |
+
"details": "Advances into series, sequences, techniques of integration, and vector calculus.",
|
170 |
+
"chapters": [
|
171 |
+
{
|
172 |
+
"chapterTitle": "Chapter 12: Vectors and the Geometry of Space",
|
173 |
+
"subChapters": [
|
174 |
+
"12.1: Three-Dimensional Coordinate Systems",
|
175 |
+
"12.2: Vectors",
|
176 |
+
"12.3: The Dot Product",
|
177 |
+
"12.4: The Cross Product",
|
178 |
+
"12.5: Equations of Lines and Planes",
|
179 |
+
"12.6: Cylinders and Quadric Surfaces"
|
180 |
+
],
|
181 |
+
"questions": []
|
182 |
+
},
|
183 |
+
{
|
184 |
+
"chapterTitle": "Chapter 13: Vector Functions",
|
185 |
+
"subChapters": [
|
186 |
+
"13.1: Vector Functions and Space Curves",
|
187 |
+
"13.2: Derivatives and Integrals of Vector Functions",
|
188 |
+
"13.3: Arc Length and Curvature",
|
189 |
+
"13.4: Motion in Space: Velocity and Acceleration"
|
190 |
+
],
|
191 |
+
"questions": []
|
192 |
+
},
|
193 |
+
{
|
194 |
+
"chapterTitle": "Chapter 14: Partial Derivatives",
|
195 |
+
"subChapters": [
|
196 |
+
"14.1: Functions of Several Variables",
|
197 |
+
"14.2: Limits and Continuity",
|
198 |
+
"14.3: Partial Derivatives",
|
199 |
+
"14.4: Tangent Planes and Linear Approximation",
|
200 |
+
"14.5: The Chain Rule"
|
201 |
+
],
|
202 |
+
"questions": []
|
203 |
+
}
|
204 |
+
]
|
205 |
+
}
|
206 |
+
]
|
207 |
+
}
|
208 |
+
|
209 |
+
def generate_question_set(self, chapter_title, subchapter_titles, num_questions=3):
|
210 |
+
"""Generate a set of questions with step-by-step solutions for a chapter."""
|
211 |
+
|
212 |
+
# Try the primary model first
|
213 |
+
self.model_manager.set_current_model(PRIMARY_MODEL)
|
214 |
+
|
215 |
+
prompt = f"""Create {num_questions} calculus questions with detailed step-by-step solutions for:
|
216 |
+
{chapter_title}
|
217 |
|
218 |
+
The questions should cover these subchapters:
|
219 |
+
{', '.join(subchapter_titles)}
|
|
|
220 |
|
221 |
For each question:
|
222 |
+
1. Write a clear, university-level calculus problem
|
223 |
+
2. Provide a comprehensive step-by-step solution with all math steps shown
|
224 |
+
3. Include a final answer
|
|
|
|
|
225 |
|
226 |
+
Format each question as:
|
227 |
+
QUESTION: [Problem statement]
|
228 |
+
SOLUTION:
|
229 |
+
Step 1: [First step with explanation]
|
230 |
+
Step 2: [Next step]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
231 |
...
|
232 |
+
Final Answer: [The solution]
|
233 |
|
234 |
+
Make sure to use proper mathematical notation and include a variety of question types.
|
235 |
"""
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
236 |
|
237 |
+
try:
|
238 |
+
generated_content = self.model_manager.generate_text(prompt, max_length=2048)
|
239 |
+
|
240 |
+
# Check if the content looks good
|
241 |
+
if len(generated_content) < 200 or "QUESTION" not in generated_content:
|
242 |
+
# Try the secondary model if the primary one gave poor results
|
243 |
+
logging.warning(f"Primary model gave insufficient results for {chapter_title}. Trying secondary model.")
|
244 |
+
self.model_manager.set_current_model(SECONDARY_MODEL)
|
245 |
+
generated_content = self.model_manager.generate_text(prompt, max_length=2048)
|
246 |
+
|
247 |
+
# Parse the generated content into question objects
|
248 |
+
questions = self.parse_questions(generated_content)
|
249 |
+
|
250 |
+
if not questions or len(questions) == 0:
|
251 |
+
logging.warning(f"Failed to parse any questions from content for {chapter_title}")
|
252 |
+
return []
|
253 |
+
|
254 |
+
return questions
|
255 |
+
|
256 |
+
except Exception as e:
|
257 |
+
logging.error(f"Error generating questions for {chapter_title}: {str(e)}")
|
258 |
+
return []
|
259 |
+
|
260 |
+
def parse_questions(self, content):
|
261 |
+
"""Parse the generated content into structured question objects."""
|
262 |
+
questions = []
|
263 |
|
264 |
+
# Split by "QUESTION:" or similar markers
|
265 |
+
parts = content.split("QUESTION:")
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
266 |
|
267 |
+
for i, part in enumerate(parts):
|
268 |
+
if i == 0:
|
269 |
+
continue # Skip the first part (before the first QUESTION:)
|
270 |
+
|
271 |
+
try:
|
272 |
+
# Split into question and solution
|
273 |
+
if "SOLUTION:" in part:
|
274 |
+
question_text, solution = part.split("SOLUTION:", 1)
|
275 |
+
else:
|
276 |
+
# Try alternative formats
|
277 |
+
for marker in ["Solution:", "STEPS:", "Steps:"]:
|
278 |
+
if marker in part:
|
279 |
+
question_text, solution = part.split(marker, 1)
|
280 |
+
break
|
281 |
+
else:
|
282 |
+
question_text = part
|
283 |
+
solution = ""
|
284 |
+
|
285 |
+
questions.append({
|
286 |
+
"question": question_text.strip(),
|
287 |
+
"solution": solution.strip()
|
288 |
+
})
|
289 |
+
except Exception as e:
|
290 |
+
logging.error(f"Error parsing question {i}: {str(e)}")
|
291 |
+
continue
|
292 |
+
|
293 |
+
return questions
|
294 |
|
295 |
+
def worker_function(self, queue, results):
|
296 |
+
"""Worker thread function to process chapters from queue."""
|
297 |
+
while True:
|
298 |
+
item = queue.get()
|
299 |
+
if item is None: # None signals to exit
|
300 |
+
queue.task_done()
|
301 |
+
break
|
302 |
+
|
303 |
+
book_idx, chapter_idx, chapter = item
|
304 |
+
chapter_title = chapter["chapterTitle"]
|
305 |
+
subchapters = chapter.get("subChapters", [])
|
306 |
+
|
307 |
+
logging.info(f"Processing: {chapter_title}")
|
308 |
+
|
309 |
+
# Try to generate questions with retries
|
310 |
+
for attempt in range(MAX_RETRIES):
|
311 |
+
try:
|
312 |
+
questions = self.generate_question_set(chapter_title, subchapters, num_questions=4)
|
313 |
+
if questions:
|
314 |
+
# Save the questions to the chapter
|
315 |
+
self.textbook_data["books"][book_idx]["chapters"][chapter_idx]["questions"] = questions
|
316 |
+
|
317 |
+
logging.info(f"✓ Generated {len(questions)} questions for {chapter_title}")
|
318 |
+
break # Success, exit retry loop
|
319 |
+
else:
|
320 |
+
logging.warning(f"No questions generated for {chapter_title} on attempt {attempt+1}")
|
321 |
+
|
322 |
+
except Exception as e:
|
323 |
+
logging.error(f"Attempt {attempt+1}/{MAX_RETRIES} failed for {chapter_title}: {str(e)}")
|
324 |
+
time.sleep(2) # Wait before retrying
|
325 |
+
|
326 |
+
# Save current state to file
|
327 |
+
self.save_current_state()
|
328 |
+
queue.task_done()
|
329 |
|
330 |
+
def save_current_state(self):
|
331 |
+
"""Save the current state of the textbook generation."""
|
332 |
+
timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
|
333 |
+
with open(os.path.join(OUTPUT_DIR, f"textbook_state_{timestamp}.json"), "w") as f:
|
334 |
+
json.dump(self.textbook_data, f, indent=2)
|
335 |
+
|
336 |
+
# Also save to a fixed filename for the latest state
|
337 |
+
with open(os.path.join(OUTPUT_DIR, "textbook_latest.json"), "w") as f:
|
338 |
+
json.dump(self.textbook_data, f, indent=2)
|
339 |
|
340 |
+
def process_in_batches(self):
|
341 |
+
"""Process all chapters in batches."""
|
342 |
+
queue = Queue()
|
|
|
343 |
|
344 |
+
# Queue all chapters for processing
|
345 |
+
for book_idx, book in enumerate(self.textbook_data["books"]):
|
346 |
+
for chapter_idx, chapter in enumerate(book["chapters"]):
|
347 |
+
queue.put((book_idx, chapter_idx, chapter))
|
348 |
|
349 |
+
# Create and start worker thread
|
350 |
+
worker = Thread(target=self.worker_function, args=(queue, None))
|
351 |
+
worker.daemon = True # Allow the program to exit even if the thread is running
|
352 |
+
worker.start()
|
353 |
|
354 |
+
# Process in batches
|
355 |
+
total_chapters = queue.qsize()
|
356 |
+
processed = 0
|
|
|
357 |
|
358 |
+
while processed < total_chapters:
|
359 |
+
# Wait for the batch to be processed
|
360 |
+
start_size = queue.qsize()
|
361 |
+
batch_size = min(BATCH_SIZE, start_size)
|
362 |
+
|
363 |
+
logging.info(f"Processing batch of {batch_size} chapters. {start_size} remaining.")
|
364 |
+
|
365 |
+
# Wait until this batch is done
|
366 |
+
while queue.qsize() > start_size - batch_size:
|
367 |
+
time.sleep(2)
|
368 |
+
|
369 |
+
processed += batch_size
|
370 |
+
logging.info(f"Batch complete. {processed}/{total_chapters} chapters processed.")
|
371 |
+
|
372 |
+
# Save current state
|
373 |
+
self.save_current_state()
|
374 |
|
375 |
+
# Signal worker to exit
|
376 |
+
queue.put(None)
|
377 |
+
worker.join()
|
378 |
|
379 |
+
# Save final state
|
380 |
+
self.save_current_state()
|
381 |
+
logging.info("All chapters processed. Textbook generation complete.")
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|
382 |
|
383 |
+
def main():
|
384 |
+
start_time = datetime.now()
|
385 |
+
logging.info(f"Starting textbook generation at {start_time}")
|
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|
386 |
|
387 |
+
generator = CalculusTextbookGenerator()
|
388 |
+
generator.process_in_batches()
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|
389 |
|
390 |
+
end_time = datetime.now()
|
391 |
+
duration = end_time - start_time
|
392 |
+
logging.info(f"Textbook generation completed in {duration}")
|
393 |
+
logging.info(f"Final textbook saved to {os.path.join(OUTPUT_DIR, 'textbook_latest.json')}")
|
394 |
|
395 |
+
if __name__ == "__main__":
|
396 |
+
main()
|
|