id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
1,880 |
\int \sqrt{(-y + 2) (y + 2)} y \cdot y \cdot y\,dy = \int y \cdot y \cdot y \sqrt{2^2 - y^2}\,dy
|
38,875 |
\frac{1}{\frac{1}{0}} = 1/(\dfrac10)
|
27,481 |
1 + t^3 - t^2 + t^2 - t + t + (-1) = t^3
|
1,699 |
(3 \cdot l + 1) \cdot (3 \cdot l + 1) = (-(3 \cdot l + 1))^2
|
-24,426 |
6 + \dfrac{6}{2} = 6 + 3 = 9
|
1,490 |
\left(0 = 4 + x \times x - y^2 - 4 \times x \implies (2 \times \left(-1\right) + x)^2 - y^2 = 0\right) \implies 0 = (x + 2 \times \left(-1\right) - y) \times (x + 2 \times (-1) + y)
|
683 |
x^2 + 4*x + 5*\left(-1\right) = x^2 + 4*x + 4 + 9*\left(-1\right) = (x + 2)^2 + 9*(-1) = (x + 2)^2 - 3^2
|
-8,939 |
17.5\% = \tfrac{1}{100}\cdot 17.5
|
-22,316 |
(n + 8)\cdot \left(3 + n\right) = 24 + n \cdot n + 11\cdot n
|
12,492 |
2/x = \frac{2*x}{x * x}
|
-16,343 |
7 \cdot 25^{\frac{1}{2}} \cdot 5^{1 / 2} = 7 \cdot 5 \cdot 5^{\frac{1}{2}} = 35 \cdot 5^{1 / 2}
|
26,228 |
31213 = 7^4 \times 13
|
9,497 |
e\times a + a\times g = a\times (g + e)
|
36,507 |
2*0.05 = \tfrac{10}{100}*1 = 1/10
|
-20,181 |
\frac{1}{s\cdot 28 + 7\cdot (-1)}\cdot (\left(-28\right)\cdot s) = 7/7\cdot \frac{1}{s\cdot 4 + \left(-1\right)}\cdot (\left(-4\right)\cdot s)
|
30,504 |
-s + 3*(2*e - 3*s) = e*6 - 10*s
|
6,673 |
(-1) + 2 \cdot \cos^2(w) = \cos(2 \cdot w)
|
-2,460 |
2\cdot \sqrt{7} = (2\cdot (-1) + 4)\cdot \sqrt{7}
|
31,273 |
WT = TW
|
582 |
\frac12 = 1 + (-1) + 1 + (-1) + 1 + \dotsm
|
27,753 |
1 - -2\cdot x + 1 = x\cdot 2
|
-22,205 |
45 \cdot (-1) + b^2 - b \cdot 4 = (b + 9 \cdot (-1)) \cdot (5 + b)
|
-5,737 |
\frac{4}{3\cdot x + 9\cdot \left(-1\right)} = \frac{4}{3\cdot (3\cdot (-1) + x)}
|
29,216 |
\frac{(-1) - 7}{\left(1 - 7\right)^3} = 1/27
|
-5,531 |
\frac{5}{(k + 8 \left(-1\right))\cdot 3} = \dfrac{1}{24 \left(-1\right) + k\cdot 3} 5
|
-7,786 |
\left(16 - 144\cdot i - 16\cdot i + 144\cdot \left(-1\right)\right)/32 = (-128 - 160\cdot i)/32 = -4 - 5\cdot i
|
-10,327 |
\frac{2 \cdot 1/2}{3 \cdot y + 5 \cdot (-1)} = \frac{2}{6 \cdot y + 10 \cdot (-1)}
|
-10,299 |
-\frac{5}{x\cdot 15 + 15\cdot (-1)} = 5/5\cdot (-\dfrac{1}{3\cdot (-1) + 3\cdot x})
|
7,738 |
x\cdot \lambda_2 + \lambda_1\cdot x = x\cdot \left(\lambda_2 + \lambda_1\right)
|
11,192 |
42/132 = \frac{6}{11}*7/12
|
11,599 |
2 \cdot 6 + 3 \cdot 5 + 2 \cdot 2 + 2 \cdot 4 = 2 \cdot (2 + 5) + (5 + 6) \cdot 2 + 2 \cdot (5 + 4) - 3 \cdot 5
|
45,199 |
2^n \sin\left(\dfrac{1}{2^n}z\right) = 2^n*(\frac{z}{2^n} - \frac{1}{3!}(\tfrac{1}{2^n}z)^2 * (\frac{1}{2^n}z) + \cdots) = z - \frac{1}{3!*2^{2n}}z^3 + \cdots
|
4,317 |
-(x - \dfrac{9}{2}) = 0 \implies x = -\frac92
|
-22,834 |
\dfrac{9 \cdot 5}{2 \cdot 9} = 45/18
|
4,710 |
\dfrac{1}{16^{3/4} \cdot 27^{2/3}} = \frac{1}{(27 \cdot 27)^{\frac{1}{3}} (16^2 \cdot 16)^{\frac14}}
|
89 |
\binom{8}{3}*\left(\frac{5}{3} + 5/4\right)*\binom{7}{2} = 3430
|
6,814 |
1 - 9/16 = \frac{1}{16} \cdot 7
|
3,090 |
|X| |B| = |X B|
|
30,414 |
2*2*7! = 7!*4
|
10,685 |
1100 = -\frac12\times 50\times 50 + 3600 - \dfrac{1}{2}\times 50\times 50
|
13,206 |
x - 1 - x = x \cdot 2 + (-1)
|
26,436 |
cf = ef \Rightarrow 0 = (-c + e) f
|
29,553 |
x!^2 \cdot (x + 1) = (x + 1)! \cdot x!
|
-18,392 |
\dfrac{s^2 + 2*s + 1}{s^2 + s*3 + 2} = \tfrac{(s + 1)*(s + 1)}{(2 + s)*\left(1 + s\right)}
|
2,943 |
e^n = e^{\frac{1}{\tfrac{1}{n}}}
|
34,697 |
n/2 \leq k\Longrightarrow n/2 \geq -k + n
|
257 |
\dfrac{k!}{(2 \cdot k)!} = ((k + 1) \cdot \dotsm \cdot 2 \cdot k)^{-1} < \frac{1}{k^k}
|
24,103 |
\frac{x!}{\left(x - s\right)! \cdot s!} = {x \choose s}
|
14,278 |
\binom{x + 1}{k} = \binom{x}{k} + \binom{x}{k + (-1)}
|
-29,100 |
9 \times (-8) = -72
|
43,051 |
|-z + H| = |-z + H|
|
3,036 |
0 + x^3 + x^2 + x \cdot 0 = \left(0 + x\right)^2 \cdot (x + 1)
|
9,131 |
(r^z + 3) \cdot (r^z + (-1)) + 4 = r^{2 \cdot z} + 2 \cdot r^z + 1 = \left(r^z + 1\right)^2
|
27,204 |
\cos\left(a - b\right) = \sin{a}\cdot \sin{b} + \cos{a}\cdot \cos{b}
|
-1,384 |
-7/3*7/2 = \frac{7*\tfrac{1}{2}}{1/7*(-3)}
|
8,539 |
\frac{\frac{1}{27}*4}{180} = 1/1215
|
54,743 |
-\int \cos(z)\,\mathrm{d}z = \int \sin(z)\cdot \sec^3(z)\,\mathrm{d}z
|
6,276 |
\int_{-e}^e b\,\mathrm{d}y = 2\cdot \int\limits_0^e b\,\mathrm{d}y
|
47,387 |
1 + H + x = x + 1 + H
|
17,512 |
\frac{\sqrt{2}}{2} = \cos(\frac{1}{4} \pi)
|
24,702 |
2\cdot \left(a_i + 2\cdot (-1)\right) = 2\cdot a_i + 4\cdot (-1) \gt a_i
|
4,621 |
0 = (2 + \sqrt{4}) (2 - \sqrt{4})
|
25,749 |
p \cdot l + k \cdot p = p \cdot (l + k)
|
-20,384 |
\frac{(-1)*4 r}{-20 r + 16 \left(-1\right)} = \frac{(-1) r}{-5r + 4(-1)} \frac44
|
3,365 |
x*(5(-1) + a) + (x + (-1)) (x^2 - x*4 + 1) = x^3 - 5x^2 + ax + (-1)
|
19,357 |
(1 - u + a\cdot u)/a = \left(1 + (-1 + a)\cdot u\right)/a = \frac{1}{a}\cdot \left(1 - (1 - a)\cdot u\right)
|
-2,213 |
-\frac{1}{14} + \frac{1}{14}\cdot 3 = 2/14
|
6,090 |
19^{17} \cdot 19^{16} \cdot 12^{17} = 12^{17} \cdot 19^{33}
|
-1,666 |
\pi \frac1613 = \pi \cdot 11/12 + 5/4 \pi
|
31,506 |
(n + (-1))/(2\cdot n) = \frac{1}{2}\cdot (1 - \frac{1}{n}) = 1/2 - 1/\left(2\cdot n\right)
|
34,861 |
(6 + 6) \times 4 = 48
|
13,745 |
3^3 + 5 \cdot 1^3 + 4 (-2)^2 (-2) = 27 + 5 - 4 \cdot 8 = 0
|
21,738 |
(3z + 1) (z + 2(-1)) = \left(z + 1/3\right) (z + 2(-1))\cdot 3
|
-16,437 |
10\times \sqrt{16}\times \sqrt{11} = 10\times 4\times \sqrt{11} = 40\times \sqrt{11}
|
25,314 |
84 + 42*(-1) = 42
|
27,905 |
(-1) + p^{32} = (p^{16} + 1) \cdot \left(p^8 + 1\right) \cdot (1 + p^4) \cdot (1 + p^2) \cdot (p + 1) \cdot \left(p + (-1)\right)
|
-1,424 |
\dfrac{1}{(-7) \cdot 1/8}((-1) \cdot 4 \cdot 1/3) = -\frac43 (-\frac87)
|
19,562 |
e^{-i \cdot l \cdot \pi} = \cos{l \cdot \pi} - i \cdot \sin{l \cdot \pi} = \left(-1\right)^l
|
9,876 |
(1 + c^{1/2}) \cdot \left(-c^{1/2} + 1\right) = 1 - c
|
-3,038 |
6^{1/2} \cdot 5 + 4 \cdot 6^{1/2} = 16^{1/2} \cdot 6^{1/2} + 6^{1/2} \cdot 25^{1/2}
|
19,389 |
87 + m^2 - 20*m = -(-2)*\frac{1}{2}*(m^2 - m*20 + 87)
|
19,577 |
2071 = 19^3 - yz\cdot 57 \implies 84 = zy
|
41,378 |
|a*b| = |b*a|
|
14,121 |
11 = (23 + (-1))/2
|
35,960 |
-(-1)^{n + \left(-1\right)} = (-1)^n
|
14,221 |
-\sqrt{2}*2 + 3 = \frac{1}{3 + \sqrt{2}*2}
|
-1,507 |
5/9 \cdot \frac{4}{3} = \dfrac{\frac{4}{3}}{9 \cdot \frac{1}{5}} \cdot 1
|
16,996 |
(1 + 2^{182}) \cdot (2^{364} - 2^{182} + 1) = 2^{546} + 1
|
5,878 |
|Y| \cdot |B| = |B \cdot Y|
|
5,146 |
-\frac{p^3}{1 + p} + 1 - p + p^2 = \frac{1}{1 + p}
|
-16,426 |
7*\sqrt{16*11} = \sqrt{176}*7
|
252 |
1/\left(b\cdot g\right) + \frac{1}{b\cdot g\cdot \left(\left(-1\right) + g\right)} = \frac{1}{b\cdot ((-1) + g)}
|
21,143 |
217 = (20 \cdot x + 3) \cdot r + \dfrac{1}{20} \cdot \left(20 \cdot x + 3 + 3 \cdot (-1)\right) = (20 \cdot x + 3) \cdot (r + 1/20) - 3/20
|
20,773 |
\left(k + 1\right)^3 + 1 = k^3 + 3\times k^2 + 3\times k + 2 \gt 4\times k^2 + 4\times k + 1
|
42,148 |
1612800 - 3\cdot 33600 = 1512000
|
13,456 |
(27*e^{i*2*x*\pi})^{1/3} = 3*(e^{i*2*x*\pi})^{\dfrac{1}{3}} = 3*e^{i*2*x*\pi/3}
|
15,394 |
\frac{7^{55}}{5^{72}} = 7 \cdot (\frac{1}{5^4} \cdot 7 \cdot 7^2)^{18}
|
22,944 |
\left(z + \left(-1\right)\right)\cdot \left(z - e^{2\cdot \pi/m}\right)\cdot \cdots\cdot e^{2\cdot \pi\cdot (\left(-1\right) + m)/m} = z^m + (-1)
|
28,870 |
C_1\cdot E_2 = C_2\cdot E_2 \Rightarrow C_1\cdot C_2 = E_2\cdot C_1\cdot 2
|
14,099 |
-b\cdot (-1) + a = a + b
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.