id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
14,912 |
|y| = \sqrt{y*\overline{y}} = \sqrt{\overline{y}*y} = |\overline{y}|
|
-7,108 |
6/15\times 6/14 = \frac{6}{35}
|
1,773 |
-x \times Y = Y \times x - x \times Y - Y \times x = (Y, x)
|
15,237 |
\tan(\dfrac12π - x) = \frac{\cos(x)}{\sin(x)} = \dfrac{1}{\tan(x)}
|
8,899 |
p^4 + p^2 + p^2 + p^2 + p^2 - p^3 - p^3 - p^3 - p^3 = 4*p * p - p * p * p*4 + p^4
|
-4,202 |
\tfrac{110}{44}*\frac{a^4}{a} = \dfrac{110*a^4}{a*44}
|
25,315 |
x! = x \cdot ((-1) + x) \cdot \left(x + 2 \cdot (-1)\right) \cdot \cdots \cdot 3 \cdot 2
|
8,324 |
x = -(1 + x)*2 + x*3 + 2
|
15,126 |
\left(g\cdot \frac{d}{g}\right)^l = g\cdot \frac1g\cdot d^l
|
20,357 |
2\cdot 3^n = \frac{1}{3 + (-1)}\cdot (3^{n + 1} + (-1)) \Rightarrow -3^n + (-1) = 0
|
-15,927 |
\dfrac{8}{10} - 8\cdot \frac{1}{10}\cdot 9 = -64/10
|
22,378 |
E*A*h = A*h*E
|
32,852 |
\frac{d}{dz} \arcsin(z) = \dfrac{1}{(1 - z \cdot z)^{1/2}}
|
28,227 |
\tfrac{1}{l + 2 \cdot (-1)} \cdot (l + 1) = 1 + \frac{3}{2 \cdot (-1) + l}
|
17,879 |
\sin(\pi/6) = \sin(5 \times \pi/6) = 1/2
|
32,171 |
\|xd\|_1 = \|xd\|_1
|
343 |
a \cdot a \cdot a - f^3 = (f^2 + a^2 + a \cdot f) \cdot (a - f)
|
42,230 |
41 = 67 + 22\cdot (-1) + 6\cdot \left(-1\right) + 2
|
723 |
(f^2 + f \cdot h + h^2) \cdot (f - h) = f^3 - h^3
|
12,353 |
-x\cdot z\cdot 2 + x^2\cdot 4 + y^2\cdot 9 + z \cdot z - 6\cdot x\cdot y - 3\cdot z\cdot y = (-z + x)^2 + \left(x - 3\cdot y\right)^2 + x^2\cdot 2 - 3\cdot y\cdot z
|
31,382 |
y = \frac{6}{\left(2(-1) + x\right)^3} \Rightarrow 6/y = (x + 2(-1))^3
|
-26,171 |
\frac{1}{3}*21 + (-1) - \frac12*12 = 7 + (-1) + 6*(-1) = 0
|
21,849 |
\sqrt{\sin^2{q} + \cos^2{q}}*f*q*a = a*q*f
|
11,803 |
\frac{k*2}{k^4}1 = \frac{2}{k^3}
|
22,717 |
\frac13(7 + 11) = 18/3 = 6
|
-20,847 |
\tfrac{6 \cdot m}{m \cdot 6} \cdot 1 \cdot (-8/3) = \frac{1}{18 \cdot m} \cdot (\left(-48\right) \cdot m)
|
16,284 |
4 = \binom{0 + 4 + (-1)}{0}*\binom{4}{3}
|
32,260 |
x^2 \cdot y^2 = (y \cdot x)^2
|
26,948 |
z^{k + \left(-1\right)} \cdot k = \frac{\partial}{\partial z} z^k
|
18,946 |
2z^2 + 2z = 2z \cdot (1 + z)
|
22,592 |
\sum_{k=1}^\infty \frac{k}{k^3} = \sum_{k=1}^\infty \frac{1}{k \cdot k}
|
30,059 |
\sum_{n=1}^{\infty} \frac{n}{(n+1)!}=\sum_{n=1}^{\infty} \frac{n+1-1}{(n+1)!}
|
28,551 |
(\sqrt{X}\cdot \sqrt{F})^2 = \sqrt{F}\cdot \sqrt{X}\cdot \sqrt{X}\cdot \sqrt{F}
|
28,620 |
\frac{7}{40} = \frac{3\cdot 7}{120}
|
-499 |
e^{\frac14\cdot \pi\cdot i\cdot 17} = (e^{\tfrac{\pi}{4}\cdot i})^{17}
|
10,199 |
-b + h = 0 \Rightarrow b = h
|
245 |
y = \dfrac{1}{z + 2} \Rightarrow z = \tfrac1y(1 - 2y)
|
-9,356 |
-2 \cdot 5 \cdot 5 + 2 \cdot 5 \cdot p = p \cdot 10 + 50 \cdot (-1)
|
26,711 |
1 - x + x^2 = -(-\frac{x^2}{2} + x) + 1 + \frac12*x * x
|
5,018 |
\frac{1}{((-1) + m)\cdot \left(2\cdot \left(-1\right) + m\right)}\cdot (4\cdot (-1) + m)\cdot (m + 3\cdot \left(-1\right)) = \frac{1}{{m + (-1) \choose 2}}\cdot {3\cdot (-1) + m \choose 2}
|
52,612 |
\frac{\sin(A)\cdot\cos(B) + \sin(B)\cdot\cos(A)}{\cos(A)\cdot\cos(B)} = \tan(A) + \tan(B)
|
14,368 |
\left\{\cdots, \left( 3, 1\right), ( 2, 0), ( 4, 2)\right\} = 2
|
19,554 |
\sqrt{x^2 + 4(-1)} - x = \frac{x^2 + 4(-1) - x^2}{\sqrt{x^2 + 4(-1)} + x} = -\frac{1}{\sqrt{x^2 + 4(-1)} + x}4
|
36,544 |
53 = 27*2 + 1 + 2*(-1)
|
-159 |
\frac{6!}{(6 + 4 \cdot (-1))! \cdot 4!} = {6 \choose 4}
|
11,423 |
\tan\left(\arctan(x) + \arctan(x^3)\right) = \frac{x + x^3}{1 - x^4} = \frac{x}{1 - x^2}
|
35,344 |
z_2 = -z_1 + 2\Longrightarrow -z_1 = z_2
|
20,034 |
x*2 - e*2 = 2 (x - e)
|
2,074 |
\sin(\pi - x \cdot \pi) = \sin(\pi \cdot x)
|
28,437 |
\dfrac{1}{x\cdot h} = \frac{1}{h\cdot x}
|
7,329 |
I_J\cdot d^2 + I_J\cdot c^2 = (c \cdot c + d^2)\cdot I_J
|
18,688 |
\sqrt{5} = \frac{l}{n}2 + (-1) = \frac1n(2l - n)
|
11,639 |
x\cdot 8 + 5\cdot (-1) = -3\cdot x \cdot x + 8\cdot x + 1 - 6 - 3\cdot x^2
|
35,055 |
e^{x \cdot 5} \cdot e^{x \cdot 5} = e^{x \cdot 10}
|
12,753 |
\sqrt{q - \sqrt{q + \sqrt{q \dotsm}}} = \left((-1) + \sqrt{1 + (q + \left(-1\right)) \cdot 4}\right)/2
|
-1,864 |
-\pi \cdot \frac{11}{6} + \pi/12 = -\pi \cdot \frac14 \cdot 7
|
20,397 |
\frac{1}{n^2}\cdot (\left(-1\right) + n^2) = -\frac{1}{n \cdot n} + 1
|
28,921 |
\frac{(-1) + x}{(-1) + x^n} = \frac{1}{(x^n + \left(-1\right))\cdot \frac{1}{x + (-1)}}
|
-1,589 |
-\pi/4 + 2*\pi = 7/4*\pi
|
-24,089 |
\tfrac{1}{6 + 10}*32 = \frac{32}{16} = \tfrac{1}{16}*32 = 2
|
25,530 |
(1 + x)^3 = 3\cdot (1^1 + 2^2 + \dots + x^2) + 3\cdot (1 + 2 + \dots + x) + x + 1
|
16,115 |
a \cdot 5 + b \cdot 5^{1 / 2} = 5^{1 / 2} \cdot (a \cdot 5^{1 / 2} + b)
|
8,415 |
h * h*k = (2*h) * (2*h)*k*0.25
|
4,363 |
1 + \cos{x} = 1 + 2\times \cos^2{\tfrac{x}{2}} + \left(-1\right) = 2\times \cos^2{x/2}
|
19,655 |
\left((-1) + r\right)\cdot r\cdot (2\cdot (-1) + r)! = r!
|
18,110 |
(-3 \cdot a + 5)^2 - 4 \cdot (a \cdot a^2 - 2 \cdot a^2 - 2 \cdot a + 4) = -4 \cdot a^3 + 17 \cdot a^2 - 22 \cdot a + 9 = (9 - 4 \cdot a) \cdot (a + (-1))^2
|
-14,778 |
84 = \tfrac{420}{5}
|
34,787 |
\binom{(-1) + n}{n - r} = \binom{(-1) + n}{r + (-1)}
|
4,170 |
\sin(3x) = \sin(x + 2x) = \sin(x) \cos\left(2x\right) + \cos(x) \sin(2x)
|
26,224 |
16 + 12*\left(-1\right) = 4
|
-2,739 |
13^{1/2}*\left(3 + 4\right) = 13^{1/2}*7
|
29,193 |
4(a \cdot a - mg \cdot g) = (a \cdot 2)^2 - (2g)^2 m
|
-8,417 |
\dfrac{1}{-3}*3 = -1
|
-9,156 |
-a \cdot 7 \cdot 7 a + 2 \cdot 5 \cdot 7 a = 70 a - 49 a^2
|
4,635 |
1 + 25 (-1) + 100 + 100 (-1) + 25 + \left(-1\right) = 0
|
24,864 |
(x^2)^{1 / 2} = (x^2)^{\frac{1}{2}} = x^{2/2} = x
|
-6,143 |
\tfrac{-r*5 + 7}{r^2*2 + 20 r + 18} = \frac{1}{18 + 2r^2 + r*20}\left(r + 9 - r*2 + 2(-1) - 4r\right)
|
6,742 |
(-1)^3 = (-1)^{6/2} = ((-1)^6)^{1/2} = 1^{\dfrac{1}{2}} = 1
|
13,738 |
\frac{1}{3} = (\dfrac{2}{3})^3 + \left(\frac{1}{3}\right) * (\dfrac{1}{3})^2
|
14,096 |
m^r = {m \choose 0} m^r
|
25,761 |
\frac98 = 3*\frac14/(2*1/3)
|
-21,657 |
-\tfrac{4}{11} = -4/11
|
-20,684 |
-\frac{3}{7} \frac{1}{(-6) q}(q*(-6)) = \frac{18 q}{(-1)*42 q}
|
37,089 |
768 = 2^8 \cdot 3
|
-2,491 |
\sqrt{8}+\sqrt{50}-\sqrt{18} = \sqrt{4 \cdot 2}+\sqrt{25 \cdot 2}-\sqrt{9 \cdot 2}
|
27,568 |
(x + y + z)^2 = x^2 + y \cdot y + z \cdot z + (x \cdot y + z \cdot x + y \cdot z) \cdot 2
|
-5,231 |
0.18 \cdot 10^{(-5) \cdot (-1) - 5} = 10^0 \cdot 0.18
|
13,677 |
0 = \frac{13 + y\cdot 4}{5 + 2y^2 + y\cdot 7} \Rightarrow 0 = 13 + 4y
|
9,319 |
\theta_1 + 2*\pi*z = 2*\theta_2 - \theta_1 \Rightarrow z*\pi + \theta_1 = \theta_2
|
26,555 |
\frac{dY}{dX} = -\frac{1}{3*X + 4*Y}*(2*X + 3*Y) = -\frac{2 + 3*\dfrac{1}{X}*Y}{3 + 4*Y/X}
|
15,769 |
\dfrac{1}{6}*\left(y^2 + y\right)*(2 + y) = \binom{2 + y}{3}
|
-12,281 |
\dfrac34 = \frac{r}{16 \cdot \pi} \cdot 16 \cdot \pi = r
|
24,587 |
\left(k + 2\right)*(k + 1)! = (k + 2)!
|
21,352 |
k\cdot z = k\cdot z
|
32,900 |
\left(e^{\frac{1}{2}\cdot t}\right)^2 = e^{\frac{t}{2}}\cdot e^{\dfrac{t}{2}} = e^t
|
21,816 |
99 z = 13 \Rightarrow z = 13/99
|
10,056 |
(3*n + 3*\left(-1\right))/3 + \frac{1}{3}*(3*n^2 + 3*n + 1) = \frac{1}{3}*(3*n^2 + 6*n + 2*(-1)) = n^2 + 2*n - 2/3
|
3,301 |
\left(x + 1 = x \Rightarrow x \cdot x = x^2 + x \cdot 2 + 1\right) \Rightarrow x \cdot 2 + 1 = 0
|
19,148 |
-2 \cdot e^{\dfrac13 \cdot (i \cdot (-1) \cdot \pi)} = -2 \cdot e^{\dfrac{1}{3} \cdot (i \cdot \pi \cdot (-1))}
|
41,378 |
|a \cdot g| = |g \cdot a|
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.