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| import gradio as gr | |
| import json | |
| import re | |
| import random | |
| import time | |
| import os | |
| from transformers import pipeline | |
| from huggingface_hub import HfApi | |
| # Set constants | |
| DEFAULT_NUM_QUESTIONS = 3 | |
| DEFAULT_DIFFICULTY = "Medium" | |
| MODEL_GENERATION = "facebook/opt-1.3b" # Free model for question generation | |
| MODEL_VERIFICATION = "gpt2-large" # Free model for verification | |
| # Initialize models (with low memory footprint) | |
| try: | |
| question_generator = pipeline("text-generation", model=MODEL_GENERATION, max_length=1000) | |
| question_verifier = pipeline("text-generation", model=MODEL_VERIFICATION, max_length=300) | |
| except Exception as e: | |
| print(f"Model loading error: {str(e)}. Will attempt to load on first use.") | |
| question_generator = None | |
| question_verifier = None | |
| # Calculus curriculum from James Stewart's textbooks | |
| calculus_curriculum = [ | |
| { | |
| "chapter": "1. Functions and Models", | |
| "subchapters": [ | |
| "1.1 Four Ways to Represent a Function", | |
| "1.2 Mathematical Models", | |
| "1.3 New Functions from Old Functions", | |
| "1.4 Exponential Functions", | |
| "1.5 Inverse Functions and Logarithms", | |
| "1.6 Parametric Curves" | |
| ], | |
| "key_formulas": [ | |
| "Domain and Range", | |
| "Function composition: $(f \\circ g)(x) = f(g(x))$", | |
| "Exponential function: $f(x) = a^x$, where $a > 0$", | |
| "Natural exponential function: $f(x) = e^x$", | |
| "Logarithmic function: $f(x) = \\log_a(x)$, where $a > 0, a \\neq 1$", | |
| "Natural logarithm: $f(x) = \\ln(x)$" | |
| ] | |
| }, | |
| { | |
| "chapter": "2. Limits and Derivatives", | |
| "subchapters": [ | |
| "2.1 The Tangent and Velocity Problems", | |
| "2.2 The Limit of a Function", | |
| "2.3 Calculating Limits", | |
| "2.4 Continuity", | |
| "2.5 The Derivative", | |
| "2.6 The Derivative as a Function", | |
| "2.7 Derivatives of Trigonometric Functions", | |
| "2.8 The Chain Rule", | |
| "2.9 Implicit Differentiation", | |
| "2.10 Related Rates", | |
| "2.11 Linear Approximations and Differentials" | |
| ], | |
| "key_formulas": [ | |
| "Limit Definition: $\\lim_{x \\to a} f(x) = L$", | |
| "Derivative Definition: $f'(x) = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h}$", | |
| "Power Rule: $\\frac{d}{dx}(x^n) = nx^{n-1}$", | |
| "Product Rule: $\\frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)$", | |
| "Quotient Rule: $\\frac{d}{dx}\\left[\\frac{f(x)}{g(x)}\\right] = \\frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$", | |
| "Chain Rule: $\\frac{d}{dx}[f(g(x))] = f'(g(x)) \\cdot g'(x)$" | |
| ] | |
| }, | |
| { | |
| "chapter": "3. Applications of Differentiation", | |
| "subchapters": [ | |
| "3.1 Maximum and Minimum Values", | |
| "3.2 The Mean Value Theorem", | |
| "3.3 How Derivatives Affect the Shape of a Graph", | |
| "3.4 Indeterminate Forms and L'Hospital's Rule", | |
| "3.5 Summary of Curve Sketching", | |
| "3.6 Optimization Problems", | |
| "3.7 Newton's Method", | |
| "3.8 Antiderivatives" | |
| ], | |
| "key_formulas": [ | |
| "Critical Points: $f'(x) = 0$ or $f'(x)$ is undefined", | |
| "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 $f'(c) = \\frac{f(b) - f(a)}{b - a}$", | |
| "Second Derivative Test: If $f'(c) = 0$ and $f''(c) > 0$, then $f$ has a local minimum at $c$", | |
| "L'Hospital's Rule: $\\lim_{x \\to a}\\frac{f(x)}{g(x)} = \\lim_{x \\to a}\\frac{f'(x)}{g'(x)}$", | |
| "Newton's Method: $x_{n+1} = x_n - \\frac{f(x_n)}{f'(x_n)}$" | |
| ] | |
| }, | |
| { | |
| "chapter": "4. Integrals", | |
| "subchapters": [ | |
| "4.1 Areas and Distances", | |
| "4.2 The Definite Integral", | |
| "4.3 The Fundamental Theorem of Calculus", | |
| "4.4 Indefinite Integrals and the Net Change Theorem", | |
| "4.5 The Substitution Rule" | |
| ], | |
| "key_formulas": [ | |
| "Definite Integral: $\\int_a^b f(x)\\,dx = \\lim_{n \\to \\infty} \\sum_{i=1}^{n} f(x_i^*)\\Delta x$", | |
| "Fundamental Theorem of Calculus: $\\int_a^b f(x)\\,dx = F(b) - F(a)$ where $F'(x) = f(x)$", | |
| "Indefinite Integral: $\\int f(x)\\,dx = F(x) + C$ where $F'(x) = f(x)$", | |
| "Power Rule for Integration: $\\int x^n\\,dx = \\frac{x^{n+1}}{n+1} + C$ for $n \\neq -1$", | |
| "Substitution Rule: $\\int f(g(x))g'(x)\\,dx = \\int f(u)\\,du$ where $u = g(x)$" | |
| ] | |
| }, | |
| { | |
| "chapter": "5. Applications of Integration", | |
| "subchapters": [ | |
| "5.1 Areas Between Curves", | |
| "5.2 Volumes", | |
| "5.3 Volumes by Cylindrical Shells", | |
| "5.4 Work", | |
| "5.5 Average Value of a Function" | |
| ], | |
| "key_formulas": [ | |
| "Area Between Curves: $\\int_a^b [f(x) - g(x)]\\,dx$ where $f(x) \\geq g(x)$", | |
| "Volume by Disk Method: $V = \\pi\\int_a^b [R(x)]^2\\,dx$", | |
| "Volume by Washer Method: $V = \\pi\\int_a^b [(R(x))^2 - (r(x))^2]\\,dx$", | |
| "Volume by Cylindrical Shells: $V = 2\\pi\\int_a^b xf(x)\\,dx$ for rotation about y-axis", | |
| "Average Value of $f$ on $[a,b]$: $f_{avg} = \\frac{1}{b-a}\\int_a^b f(x)\\,dx$", | |
| "Work: $W = \\int_a^b F(x)\\,dx$" | |
| ] | |
| }, | |
| { | |
| "chapter": "6. Techniques of Integration", | |
| "subchapters": [ | |
| "6.1 Integration by Parts", | |
| "6.2 Trigonometric Integrals", | |
| "6.3 Trigonometric Substitution", | |
| "6.4 Integration of Rational Functions by Partial Fractions", | |
| "6.5 Strategy for Integration", | |
| "6.6 Approximate Integration", | |
| "6.7 Improper Integrals" | |
| ], | |
| "key_formulas": [ | |
| "Integration by Parts: $\\int u\\,dv = uv - \\int v\\,du$", | |
| "Trigonometric Integrals: $\\int \\sin^n x \\cos^m x\\,dx$ (various formulas)", | |
| "Trig Substitution: $x = a\\sin\\theta$ for $\\sqrt{a^2-x^2}$, $x = a\\tan\\theta$ for $\\sqrt{a^2+x^2}$", | |
| "Partial Fractions: $\\frac{P(x)}{Q(x)} = \\frac{A}{(x-a)} + \\frac{B}{(x-a)^2} + \\frac{Cx+D}{x^2+bx+c} + ...$", | |
| "Improper Integrals: $\\int_a^{\\infty} f(x)\\,dx = \\lim_{t \\to \\infty} \\int_a^t f(x)\\,dx$" | |
| ] | |
| }, | |
| { | |
| "chapter": "7. Differential Equations", | |
| "subchapters": [ | |
| "7.1 Modeling with Differential Equations", | |
| "7.2 Direction Fields and Euler's Method", | |
| "7.3 Separable Equations", | |
| "7.4 Models for Population Growth", | |
| "7.5 Linear Equations", | |
| "7.6 Predator-Prey Systems" | |
| ], | |
| "key_formulas": [ | |
| "General form of a first-order differential equation: $\\frac{dy}{dx} = f(x, y)$", | |
| "Separable equation: $\\frac{dy}{dx} = g(x)h(y)$ → $\\int \\frac{1}{h(y)}dy = \\int g(x)dx + C$", | |
| "First-order linear differential equation: $\\frac{dy}{dx} + P(x)y = Q(x)$", | |
| "Integrating factor method: Multiply by $e^{\\int P(x)dx}$", | |
| "Euler's Method: $y_{n+1} = y_n + hf(x_n, y_n)$" | |
| ] | |
| }, | |
| { | |
| "chapter": "8. Infinite Sequences and Series", | |
| "subchapters": [ | |
| "8.1 Sequences", | |
| "8.2 Series", | |
| "8.3 The Integral Test and Estimates of Sums", | |
| "8.4 The Comparison Tests", | |
| "8.5 Alternating Series", | |
| "8.6 Absolute Convergence and the Ratio and Root Tests", | |
| "8.7 Strategy for Testing Series", | |
| "8.8 Power Series", | |
| "8.9 Representations of Functions as Power Series", | |
| "8.10 Taylor and Maclaurin Series" | |
| ], | |
| "key_formulas": [ | |
| "Geometric Series: $\\sum_{n=0}^{\\infty} ar^n = \\frac{a}{1-r}$ if $|r| < 1$", | |
| "Taylor Series: $f(x) = \\sum_{n=0}^{\\infty} \\frac{f^{(n)}(a)}{n!}(x-a)^n$", | |
| "Maclaurin Series: $f(x) = \\sum_{n=0}^{\\infty} \\frac{f^{(n)}(0)}{n!}x^n$", | |
| "Common Maclaurin Series: $e^x = \\sum_{n=0}^{\\infty} \\frac{x^n}{n!}$, $\\sin(x) = \\sum_{n=0}^{\\infty} \\frac{(-1)^n}{(2n+1)!}x^{2n+1}$", | |
| "Ratio Test: $\\lim_{n \\to \\infty} |\\frac{a_{n+1}}{a_n}| < 1$ implies convergence" | |
| ] | |
| }, | |
| { | |
| "chapter": "9. Parametric Equations and Polar Coordinates", | |
| "subchapters": [ | |
| "9.1 Parametric Curves", | |
| "9.2 Calculus with Parametric Curves", | |
| "9.3 Polar Coordinates", | |
| "9.4 Areas and Lengths in Polar Coordinates", | |
| "9.5 Conic Sections" | |
| ], | |
| "key_formulas": [ | |
| "Parametric curve: $x = f(t)$, $y = g(t)$", | |
| "Arc length of parametric curve: $L = \\int_a^b \\sqrt{[f'(t)]^2 + [g'(t)]^2}\\,dt$", | |
| "Polar to rectangular coordinates: $x = r\\cos\\theta$, $y = r\\sin\\theta$", | |
| "Rectangular to polar coordinates: $r = \\sqrt{x^2 + y^2}$, $\\theta = \\arctan(\\frac{y}{x})$", | |
| "Area in polar coordinates: $A = \\frac{1}{2}\\int_{\\alpha}^{\\beta} [r(\\theta)]^2\\,d\\theta$" | |
| ] | |
| }, | |
| { | |
| "chapter": "10. Vectors and the Geometry of Space", | |
| "subchapters": [ | |
| "10.1 Three-Dimensional Coordinate Systems", | |
| "10.2 Vectors", | |
| "10.3 The Dot Product", | |
| "10.4 The Cross Product", | |
| "10.5 Equations of Lines and Planes", | |
| "10.6 Cylinders and Quadric Surfaces" | |
| ], | |
| "key_formulas": [ | |
| "Dot Product: $\\vec{a} \\cdot \\vec{b} = |\\vec{a}||\\vec{b}|\\cos\\theta$", | |
| "Cross Product: $\\vec{a} \\times \\vec{b} = |\\vec{a}||\\vec{b}|\\sin\\theta\\,\\vec{n}$", | |
| "Equation of a line: $\\vec{r} = \\vec{r_0} + t\\vec{v}$", | |
| "Equation of a plane: $\\vec{n} \\cdot (\\vec{r} - \\vec{r_0}) = 0$ or $ax + by + cz + d = 0$", | |
| "Distance from point to plane: $d = \\frac{|ax_0 + by_0 + cz_0 + d|}{\\sqrt{a^2 + b^2 + c^2}}$" | |
| ] | |
| }, | |
| { | |
| "chapter": "11. Vector Functions", | |
| "subchapters": [ | |
| "11.1 Vector Functions and Space Curves", | |
| "11.2 Derivatives and Integrals of Vector Functions", | |
| "11.3 Arc Length and Curvature", | |
| "11.4 Motion in Space: Velocity and Acceleration" | |
| ], | |
| "key_formulas": [ | |
| "Vector function: $\\vec{r}(t) = x(t)\\vec{i} + y(t)\\vec{j} + z(t)\\vec{k}$", | |
| "Derivative of vector function: $\\vec{r}'(t) = x'(t)\\vec{i} + y'(t)\\vec{j} + z'(t)\\vec{k}$", | |
| "Arc length: $L = \\int_a^b |\\vec{r}'(t)|\\,dt$", | |
| "Unit tangent vector: $\\vec{T}(t) = \\frac{\\vec{r}'(t)}{|\\vec{r}'(t)|}$", | |
| "Curvature: $\\kappa = \\frac{|\\vec{T}'(t)|}{|\\vec{r}'(t)|}$", | |
| "Acceleration: $\\vec{a}(t) = \\vec{r}''(t)$" | |
| ] | |
| }, | |
| { | |
| "chapter": "12. Partial Derivatives", | |
| "subchapters": [ | |
| "12.1 Functions of Several Variables", | |
| "12.2 Limits and Continuity", | |
| "12.3 Partial Derivatives", | |
| "12.4 Tangent Planes and Linear Approximations", | |
| "12.5 The Chain Rule", | |
| "12.6 Directional Derivatives and the Gradient Vector", | |
| "12.7 Maximum and Minimum Values", | |
| "12.8 Lagrange Multipliers" | |
| ], | |
| "key_formulas": [ | |
| "Partial derivative: $\\frac{\\partial f}{\\partial x}(x_0, y_0)$", | |
| "Gradient: $\\nabla f = \\frac{\\partial f}{\\partial x}\\vec{i} + \\frac{\\partial f}{\\partial y}\\vec{j} + \\frac{\\partial f}{\\partial z}\\vec{k}$", | |
| "Directional derivative: $D_\\vec{u}f = \\nabla f \\cdot \\vec{u}$", | |
| "Tangent plane: $z - z_0 = f_x(x_0, y_0)(x - x_0) + f_y(x_0, y_0)(y - y_0)$", | |
| "Chain Rule: $\\frac{dz}{dt} = \\frac{\\partial z}{\\partial x}\\frac{dx}{dt} + \\frac{\\partial z}{\\partial y}\\frac{dy}{dt}$" | |
| ] | |
| }, | |
| { | |
| "chapter": "13. Multiple Integrals", | |
| "subchapters": [ | |
| "13.1 Double Integrals over Rectangles", | |
| "13.2 Iterated Integrals", | |
| "13.3 Double Integrals over General Regions", | |
| "13.4 Double Integrals in Polar Coordinates", | |
| "13.5 Applications of Double Integrals", | |
| "13.6 Triple Integrals", | |
| "13.7 Triple Integrals in Cylindrical Coordinates", | |
| "13.8 Triple Integrals in Spherical Coordinates", | |
| "13.9 Change of Variables in Multiple Integrals" | |
| ], | |
| "key_formulas": [ | |
| "Double integral: $\\iint_R f(x,y)\\,dA = \\int_a^b \\int_c^d f(x,y)\\,dy\\,dx$", | |
| "Area in polar coordinates: $\\iint_R f(r,\\theta)\\,dA = \\int_{\\alpha}^{\\beta} \\int_{h_1(\\theta)}^{h_2(\\theta)} f(r,\\theta)\\,r\\,dr\\,d\\theta$", | |
| "Triple integral: $\\iiint_E f(x,y,z)\\,dV$", | |
| "Cylindrical coordinates: $\\iiint_E f(x,y,z)\\,dV = \\iiint_E f(r\\cos\\theta, r\\sin\\theta, z)\\,r\\,dr\\,d\\theta\\,dz$", | |
| "Spherical coordinates: $\\iiint_E f(x,y,z)\\,dV = \\iiint_E f(\\rho\\sin\\phi\\cos\\theta, \\rho\\sin\\phi\\sin\\theta, \\rho\\cos\\phi)\\,\\rho^2\\sin\\phi\\,d\\rho\\,d\\phi\\,d\\theta$" | |
| ] | |
| }, | |
| { | |
| "chapter": "14. Vector Calculus", | |
| "subchapters": [ | |
| "14.1 Vector Fields", | |
| "14.2 Line Integrals", | |
| "14.3 The Fundamental Theorem for Line Integrals", | |
| "14.4 Green's Theorem", | |
| "14.5 Curl and Divergence", | |
| "14.6 Surface Integrals", | |
| "14.7 Stokes' Theorem", | |
| "14.8 The Divergence Theorem" | |
| ], | |
| "key_formulas": [ | |
| "Line integral of scalar function: $\\int_C f(x,y,z)\\,ds = \\int_a^b f(\\vec{r}(t))|\\vec{r}'(t)|\\,dt$", | |
| "Line integral of vector field: $\\int_C \\vec{F} \\cdot d\\vec{r} = \\int_a^b \\vec{F}(\\vec{r}(t)) \\cdot \\vec{r}'(t)\\,dt$", | |
| "Green's Theorem: $\\oint_C (P\\,dx + Q\\,dy) = \\iint_D (\\frac{\\partial Q}{\\partial x} - \\frac{\\partial P}{\\partial y})\\,dA$", | |
| "Divergence: $\\text{div}\\,\\vec{F} = \\nabla \\cdot \\vec{F} = \\frac{\\partial P}{\\partial x} + \\frac{\\partial Q}{\\partial y} + \\frac{\\partial R}{\\partial z}$", | |
| "Curl: $\\text{curl}\\,\\vec{F} = \\nabla \\times \\vec{F}$", | |
| "Stokes' Theorem: $\\int_S (\\nabla \\times \\vec{F}) \\cdot d\\vec{S} = \\oint_C \\vec{F} \\cdot d\\vec{r}$", | |
| "Divergence Theorem: $\\iiint_E (\\nabla \\cdot \\vec{F})\\,dV = \\iint_{\\partial E} \\vec{F} \\cdot d\\vec{S}$" | |
| ] | |
| } | |
| ] | |
| def load_models_if_needed(): | |
| """Ensures models are loaded when needed""" | |
| global question_generator, question_verifier | |
| if question_generator is None: | |
| try: | |
| question_generator = pipeline("text-generation", model=MODEL_GENERATION, max_length=1000) | |
| except Exception as e: | |
| return f"Error loading question generator: {str(e)}" | |
| if question_verifier is None: | |
| try: | |
| question_verifier = pipeline("text-generation", model=MODEL_VERIFICATION, max_length=300) | |
| except Exception as e: | |
| return f"Error loading question verifier: {str(e)}" | |
| return None | |
| def get_chapter_summary(chapter_idx, subchapter_idx=None): | |
| """Get summary of selected chapter and subchapter""" | |
| if chapter_idx < 0 or chapter_idx >= len(calculus_curriculum): | |
| return "Invalid chapter selection." | |
| chapter = calculus_curriculum[chapter_idx] | |
| if subchapter_idx is None or subchapter_idx < 0 or subchapter_idx >= len(chapter["subchapters"]): | |
| # Return chapter summary only | |
| summary = f"# {chapter['chapter']}\n\n" | |
| summary += "## Key Formulas\n" | |
| for formula in chapter.get("key_formulas", []): | |
| summary += f"- {formula}\n" | |
| return summary | |
| # Return specific subchapter | |
| subchapter = chapter["subchapters"][subchapter_idx] | |
| summary = f"# {chapter['chapter']}\n## {subchapter}\n\n" | |
| summary += "### Key Formulas\n" | |
| for formula in chapter.get("key_formulas", []): | |
| summary += f"- {formula}\n" | |
| return summary | |
| def generate_question_prompt(chapter, subchapter, difficulty, num_questions=3): | |
| """Generate a prompt for the model to create questions""" | |
| prompt = f"""Create {num_questions} university-level mathematics questions about {subchapter} from {chapter} at {difficulty} difficulty. | |
| For each question: | |
| 1. Write a clear, university-level calculus problem that requires understanding of the concepts and techniques. | |
| 2. Include a step-by-step solution showing all work and mathematical reasoning. | |
| 3. Provide the final answer. | |
| Format your response exactly as follows: | |
| ## Question 1 | |
| [Question text] | |
| ### Solution | |
| Step 1: [First step of solution] | |
| Step 2: [Second step] | |
| ... | |
| ### Answer | |
| [Final answer] | |
| ## Question 2 | |
| ... | |
| Make sure all mathematics is correct and your solution steps are clear and logical. | |
| """ | |
| return prompt | |
| def verify_question(question_text, solution_text): | |
| """Verify if the question and solution are mathematically sound""" | |
| error_msg = load_models_if_needed() | |
| if error_msg: | |
| return False, error_msg | |
| verification_prompt = f"""Verify if this calculus question and solution are mathematically correct: | |
| Question: {question_text} | |
| Solution: {solution_text} | |
| Is the solution mathematically correct? Answer Yes or No and briefly explain why.""" | |
| try: | |
| # Get verification response | |
| verification = question_verifier(verification_prompt, max_length=300)[0]['generated_text'] | |
| # Check response for indication that the solution is correct | |
| if "yes" in verification.lower() and "incorrect" not in verification.lower() and "error" not in verification.lower(): | |
| return True, "Verification passed" | |
| else: | |
| # Extract the explanation for why it's incorrect | |
| explanation = verification.split("No")[1] if "No" in verification else "Unable to determine specific issue" | |
| return False, f"Verification failed: {explanation}" | |
| except Exception as e: | |
| return False, f"Error during verification: {str(e)}" | |
| def generate_questions(chapter_index, subchapter_index, difficulty, num_questions): | |
| """Generate mathematics questions based on chapter/subchapter""" | |
| error_msg = load_models_if_needed() | |
| if error_msg: | |
| return f"## Error Loading Models\n\n{error_msg}\n\nPlease try again later or contact the administrator." | |
| # Get chapter and subchapter information | |
| if chapter_index < 0 or chapter_index >= len(calculus_curriculum): | |
| return "Please select a valid chapter." | |
| chapter = calculus_curriculum[chapter_index] | |
| if subchapter_index < 0 or subchapter_index >= len(chapter["subchapters"]): | |
| return "Please select a valid subchapter." | |
| subchapter = chapter["subchapters"][subchapter_index] | |
| # Generate prompt for the model | |
| prompt = generate_question_prompt(chapter["chapter"], subchapter, difficulty, num_questions) | |
| try: | |
| # Generate questions | |
| result = question_generator(prompt, max_length=1500, do_sample=True, | |
| temperature=0.7, top_p=0.85, num_return_sequences=1)[0]['generated_text'] | |
| # Extract generated questions and solutions | |
| result = result.replace(prompt, "") | |
| # Basic formatting fixes | |
| result = re.sub(r'#+\s*Question', '## Question', result) | |
| result = re.sub(r'#+\s*Solution', '### Solution', result) | |
| result = re.sub(r'#+\s*Answer', '### Answer', result) | |
| # Check if we got properly formatted output | |
| if "## Question" not in result: | |
| # Fallback to template questions for the topic | |
| result = generate_fallback_questions(chapter["chapter"], subchapter, num_questions) | |
| # Add chapter summary at the top | |
| summary = get_chapter_summary(chapter_index, subchapter_index) | |
| result = f"{summary}\n\n# Generated Questions\n\n{result}" | |
| return result | |
| except Exception as e: | |
| return f"Error generating questions: {str(e)}\n\nPlease try again or select a different topic." | |
| def generate_fallback_questions(chapter, subchapter, num_questions): | |
| """Generate fallback questions when model generation fails""" | |
| # Basic templates for different calculus topics | |
| if "Limits" in chapter or "Limits" in subchapter: | |
| questions = [ | |
| { | |
| "question": "Evaluate the limit: $\\lim_{x \\to 2} \\frac{x^3 - 8}{x - 2}$", | |
| "solution": "Step 1: Note that this is an indeterminate form (0/0) when x = 2.\n" + | |
| "Step 2: Factor the numerator: $x^3 - 8 = (x - 2)(x^2 + 2x + 4)$\n" + | |
| "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" + | |
| "Step 4: Evaluate by direct substitution: $2^2 + 2(2) + 4 = 4 + 4 + 4 = 12$", | |
| "answer": "12" | |
| }, | |
| { | |
| "question": "Find the limit: $\\lim_{x \\to 0} \\frac{\\sin(3x)}{x}$", | |
| "solution": "Step 1: Rewrite using the limit property $\\lim_{x \\to 0} \\frac{\\sin x}{x} = 1$\n" + | |
| "Step 2: $\\lim_{x \\to 0} \\frac{\\sin(3x)}{x} = \\lim_{x \\to 0} 3 \\cdot \\frac{\\sin(3x)}{3x}$\n" + | |
| "Step 3: Apply the limit property: $3 \\cdot \\lim_{x \\to 0} \\frac{\\sin(3x)}{3x} = 3 \\cdot 1 = 3$", | |
| "answer": "3" | |
| } | |
| ] | |
| elif "Derivative" in chapter or "Derivative" in subchapter: | |
| questions = [ | |
| { | |
| "question": "Find the derivative of $f(x) = x^3\\ln(x) - \\frac{x^3}{3}$", | |
| "solution": "Step 1: Use the product rule on $x^3\\ln(x)$\n" + | |
| "$\\frac{d}{dx}[x^3\\ln(x)] = x^3 \\cdot \\frac{1}{x} + \\ln(x) \\cdot 3x^2$\n" + | |
| "$= x^2 + 3x^2\\ln(x)$\n" + | |
| "Step 2: Find the derivative of $\\frac{x^3}{3}$\n" + | |
| "$\\frac{d}{dx}[\\frac{x^3}{3}] = \\frac{3x^2}{3} = x^2$\n" + | |
| "Step 3: Combine the results\n" + | |
| "$f'(x) = x^2 + 3x^2\\ln(x) - x^2 = 3x^2\\ln(x)$", | |
| "answer": "$f'(x) = 3x^2\\ln(x)$" | |
| } | |
| ] | |
| elif "Integration" in chapter or "Integral" in chapter or "Integration" in subchapter or "Integral" in subchapter: | |
| questions = [ | |
| { | |
| "question": "Evaluate the integral: $\\int x^2\\ln(x) dx$", | |
| "solution": "Step 1: Use integration by parts with $u = \\ln(x)$ and $dv = x^2 dx$\n" + | |
| "Then $du = \\frac{1}{x}dx$ and $v = \\frac{x^3}{3}$\n" + | |
| "Step 2: Apply the formula $\\int u dv = uv - \\int v du$\n" + | |
| "$\\int x^2\\ln(x) dx = \\ln(x) \\cdot \\frac{x^3}{3} - \\int \\frac{x^3}{3} \\cdot \\frac{1}{x} dx$\n" + | |
| "$= \\frac{x^3\\ln(x)}{3} - \\frac{1}{3}\\int x^2 dx$\n" + | |
| "$= \\frac{x^3\\ln(x)}{3} - \\frac{1}{3} \\cdot \\frac{x^3}{3} + C$\n" + | |
| "$= \\frac{x^3\\ln(x)}{3} - \\frac{x^3}{9} + C$", | |
| "answer": "$\\frac{x^3\\ln(x)}{3} - \\frac{x^3}{9} + C$" | |
| } | |
| ] | |
| else: | |
| # Generic calculus questions | |
| questions = [ | |
| { | |
| "question": "Find the critical points of $f(x) = x^3 - 6x^2 + 12x + 5$ and determine their nature.", | |
| "solution": "Step 1: Find the derivative: $f'(x) = 3x^2 - 12x + 12$\n" + | |
| "Step 2: Set $f'(x) = 0$ and solve: $3x^2 - 12x + 12 = 0$\n" + | |
| "Step 3: Simplify: $x^2 - 4x + 4 = 0$\n" + | |
| "Step 4: Factor: $(x - 2)^2 = 0$\n" + | |
| "Step 5: Therefore $x = 2$ is a critical point (with multiplicity 2)\n" + | |
| "Step 6: Find the second derivative: $f''(x) = 6x - 12$\n" + | |
| "Step 7: Evaluate at $x = 2$: $f''(2) = 6(2) - 12 = 0$\n" + | |
| "Step 8: Since $f''(2) = 0$, the second derivative test is inconclusive\n" + | |
| "Step 9: Checking $f'(x)$ around $x = 2$:\n" + | |
| "For $x < 2$, $f'(x) < 0$ and for $x > 2$, $f'(x) > 0$\n" + | |
| "Step 10: Therefore, $x = 2$ is a point of inflection", | |
| "answer": "$x = 2$ is a critical point and an inflection point" | |
| } | |
| ] | |
| # Get a random subset of questions or duplicate if we need more | |
| result_questions = [] | |
| for i in range(num_questions): | |
| idx = i % len(questions) | |
| q = questions[idx] | |
| result_questions.append({ | |
| "id": i+1, | |
| "question": q["question"], | |
| "solution": q["solution"], | |
| "answer": q["answer"] | |
| }) | |
| # Format the output | |
| result = "" | |
| for q in result_questions: | |
| result += f"## Question {q['id']}\n{q['question']}\n\n" | |
| result += f"### Solution\n{q['solution']}\n\n" | |
| result += f"### Answer\n{q['answer']}\n\n" | |
| return result | |
| def on_chapter_change(chapter_index): | |
| """Update subchapter dropdown based on selected chapter""" | |
| if chapter_index < 0 or chapter_index >= len(calculus_curriculum): | |
| return gr.Dropdown(choices=[], value=None) | |
| subchapters = calculus_curriculum[chapter_index]["subchapters"] | |
| return gr.Dropdown(choices=subchapters, value=subchapters[0] if subchapters else None) | |
| def create_interface(): | |
| """Create the Gradio interface""" | |
| # Extract chapter titles for dropdown | |
| chapters = [chapter["chapter"] for chapter in calculus_curriculum] | |
| with gr.Blocks(title="Calculus Question Generator", theme=gr.themes.Soft()) as demo: | |
| gr.Markdown("# 🧮 Calculus Question Generator") | |
| gr.Markdown("Generate university-level calculus questions with step-by-step solutions.") | |
| with gr.Row(): | |
| with gr.Column(scale=2): | |
| chapter_dropdown = gr.Dropdown( | |
| choices=chapters, | |
| value=chapters[0] if chapters else None, | |
| label="Chapter", | |
| info="Select a chapter from Stewart's Calculus" | |
| ) | |
| subchapter_dropdown = gr.Dropdown( | |
| choices=calculus_curriculum[0]["subchapters"] if calculus_curriculum else [], | |
| value=calculus_curriculum[0]["subchapters"][0] if calculus_curriculum and calculus_curriculum[0]["subchapters"] else None, | |
| label="Subchapter", | |
| info="Select a specific subchapter" | |
| ) | |
| with gr.Row(): | |
| num_questions = gr.Slider( | |
| minimum=1, | |
| maximum=5, | |
| value=DEFAULT_NUM_QUESTIONS, | |
| step=1, | |
| label="Number of Questions" | |
| ) | |
| difficulty = gr.Dropdown( | |
| choices=["Easy", "Medium", "Hard", "Advanced"], | |
| value=DEFAULT_DIFFICULTY, | |
| label="Difficulty Level" | |
| ) | |
| generate_button = gr.Button("Generate Questions", variant="primary") | |
| output = gr.Markdown(label="Generated Questions & Solutions") | |
| # Handle chapter selection change | |
| chapter_dropdown.change( | |
| fn=on_chapter_change, | |
| inputs=[chapter_dropdown], | |
| outputs=[subchapter_dropdown] | |
| ) | |
| # Handle generate button click | |
| generate_button.click( | |
| fn=generate_questions, | |
| inputs=[ | |
| gr.State(lambda: chapters.index(chapter_dropdown.value) if chapter_dropdown.value in chapters else 0), | |
| 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), | |
| difficulty, | |
| num_questions | |
| ], | |
| outputs=[output] | |
| ) | |
| gr.Markdown("---") | |
| gr.Markdown("Created by Kamagelo Mosia | Based on James Stewart's Calculus curriculum") | |
| return demo | |
| # Create and launch the interface | |
| demo = create_interface() | |
| demo.launch() |