id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
19,713 |
0 = \cos{0}*\sin{0}
|
-2,831 |
9^{1/2} \cdot 2^{1/2} - 2^{1/2} = -2^{1/2} + 3 \cdot 2^{1/2}
|
-28,782 |
\int\dfrac{\cos^2x}{1-\sin x}\,dx=\int\dfrac{(1-\sin x)(1+\sin x)}{1-\sin x}\,dx=\int(1+\sin x)\,dx
|
13,767 |
(31415 - 3\cdot 10^4)\cdot 10 + 9 = 14159
|
-9,430 |
8 \cdot z^2 + 8 \cdot z = 2 \cdot 2 \cdot 2 \cdot z + 2 \cdot 2 \cdot 2 \cdot z \cdot z
|
3,251 |
(b + x) c = xc + cb
|
-5,074 |
7.8/10 = \frac{0.78}{1000} \cdot 1 = \frac{1}{10000} \cdot 7.8
|
6,343 |
0 + C \cdot A = C \cdot A
|
-9,433 |
2*3*x - 2*2*5*x*x = 6*x - 20*x * x
|
23,913 |
\left(L - J = M - x \implies L - M = -x + J\right) \implies x - J = M - L
|
603 |
1 + \dfrac{1}{3} \times (z^2 + 4 \times \left(-1\right)) = -\frac{1}{3} + z^2/3
|
7,524 |
11\cdot \pi/8 = 3\cdot \pi/8 + \pi
|
-18,431 |
\frac{(3 + x)\cdot \left(x + 7\cdot (-1)\right)}{x\cdot (x + 7\cdot (-1))} = \frac{x^2 - 4\cdot x + 21\cdot (-1)}{-x\cdot 7 + x \cdot x}
|
-12,624 |
46 = \frac{230}{5}
|
26,674 |
{d+1 \choose 2} = {d \choose 2} + d
|
-18,967 |
2/15 = \frac{x_s}{9 \cdot \pi} \cdot 9 \cdot \pi = x_s
|
-16,896 |
7 = 5 \cdot r^2 - 20 \cdot r + 7 \cdot r + 7 \cdot (-4) = 5 \cdot r^2 - 20 \cdot r + 7 \cdot r + 28 \cdot (-1)
|
-27,602 |
\frac{1}{5*2} = 10^{-1}
|
10,222 |
0 = y_2 + 2x_1 - x_2 - z_2 \Rightarrow -z_2 + 2x_1 - x_2 = -y_2
|
33,949 |
\left(1 + x\right)\cdot (1 - x) = 1 - x^2
|
-11,707 |
16^{-\frac12} = \left(1/16\right)^{\frac{1}{2}}
|
8,443 |
1/15 = \frac{7!}{10!} \cdot 3! \cdot 8
|
20,339 |
l\cdot 2 + (-1) = l^2 - \left((-1) + l\right)^2
|
30,415 |
\sin{x} \cdot \cos{y} + \sin{y} \cdot \cos{x} = \sin(y + x)
|
11,825 |
((-1) + z)^2 + \left(-1\right) = z \cdot z - 2\cdot z
|
5,915 |
13!/\left(10!\cdot 3!\right) = \frac{13!}{3!\cdot 10!} = 286
|
8,183 |
-\int\limits_0^1 \frac{1}{x^{\alpha + 3\cdot (-1)}}\,\mathrm{d}x = -\int\limits_0^1 x^{-\alpha + 3}\,\mathrm{d}x
|
16,047 |
y^4 + 2*(-1) = \left(y^2 + \sqrt{2}\right)*(2^{\frac{1}{4}} + y)*(y - 2^{1/4})
|
53,567 |
\int_1^{10} \pi\cdot \sqrt{v}/18\,dv = \left(\int_1^{10} v^{1/2}\,dv\right)\cdot \pi/18
|
-26,154 |
e^{12}\cdot 6 - e^6\cdot 6 = 6\cdot (e^{12} - e^6)
|
27,442 |
x + y + x \times y = 10 \times x + y \Rightarrow x \times y = 9 \times x
|
30,299 |
\mathbb{E}(YR) = \mathbb{E}(Y) \mathbb{E}(R)
|
9,714 |
10 + s^2 + 6s = 1 + (s + 3) \cdot (s + 3)
|
-3,056 |
-\sqrt{4*7} + \sqrt{25*7} = \sqrt{175} - \sqrt{28}
|
35,832 |
33461 \times 33461 = 23661^2 + 23660^2
|
4,217 |
\frac{9\cdot 10}{3!}\cdot 8 = 120
|
15,541 |
2\cdot z + 5\cdot y + 1 = 2\cdot z + 5\cdot y + 5 + 4\cdot (-1) = 2\cdot \left(z + 2\cdot (-1)\right) + 5\cdot (y + 1)
|
666 |
19 = \tfrac{1}{10}\cdot 100 + \frac{1}{10}9\cdot 10
|
44,047 |
1^3 + 6*1^2 + 11 + 6 = 24 = 3*8
|
11,121 |
\binom{2\times n + (-1) - k + 1}{k} = \binom{-k + 2\times n}{k}
|
-8,850 |
9 \cdot 7 = 63
|
18,130 |
37^2-35^2=13^2-5^2=12^2
|
7,751 |
\pi\cdot 2 = 2\cdot (-\operatorname{atan}(-\infty) + \operatorname{atan}\left(\infty\right))
|
35,040 |
\frac{1}{2} \cdot 4! = 24/2 = 12 = 3 \cdot 2^2
|
8,972 |
r/q = \frac1qr
|
-30,583 |
7*(3 + x * x) = x^2*7 + 21
|
5,012 |
\int ((-1) + u)*\sqrt{u}\,du = \int (-u^{1/2} + u^{3/2})\,du
|
-15,747 |
\dfrac{s}{\frac{1}{n^{15}} s^{25}} = \tfrac{1}{\frac{1}{\frac{1}{s^{25}} n^{15}}}s
|
-10,602 |
\dfrac{2}{2\left(-1\right) + n} \frac44 = \dfrac{8}{n \cdot 4 + 8(-1)}
|
27,927 |
2 = (23^{\frac{1}{2}} + 5) \cdot (5 - 23^{\frac{1}{2}})
|
10,999 |
\int (1 - e^{-z}) e^{e^z}\,\mathrm{d}z = \int (e^z + (-1)) e^{-z} e^{e^z}\,\mathrm{d}z = \int (e^z + (-1)) e^{e^z - z}\,\mathrm{d}z
|
-103 |
30 + 5 = 35
|
7,778 |
2y^2 + 3y^2 = 5y^2 = 0 \Rightarrow 0 = y
|
12,437 |
(-1)^{\frac1n} = \left(e^{\pi i}\right)^{\frac1n} = e^{\pi i/n}
|
37,844 |
3 = 2 + 1 + 0 + 0*\dotsm
|
25,236 |
L \cdot L^2 = L \cdot L L
|
12,982 |
a + f \cdot 4 + g \cdot 3 = 0 \Rightarrow a = -4 \cdot f - g \cdot 3
|
-23,114 |
-\frac{4}{3}*8/3 = -32/9
|
18,075 |
-i*3 + 2 = (2/(\sqrt{13}) + i*(-3/\left(\sqrt{13}\right))) \sqrt{13}
|
11,652 |
\left(n*3 + (-1)\right)^{\frac13} = x \Rightarrow x^3 + 1 = 3 n
|
9,188 |
648 = 9 \left(-1\right) + 900 + 81 (-1) + 81 \left(-1\right) + 81 \left(-1\right)
|
10,873 |
3/5\cdot \frac{1}{5}\cdot 3 = \tfrac{9}{25}
|
6,095 |
b^2 + (a + 3 (-1))^2 = a^2 + \left(b + 3 (-1)\right)^2 rightarrow b = a
|
14,615 |
(-1) + y^{2^n} = (1 + y^{2^{n + \left(-1\right)}})\cdot ((-1) + y^{2^{(-1) + n}})
|
-2,252 |
\frac{1}{20}*7 = -\frac{2}{20} + \frac{1}{20}*9
|
-4,396 |
p^3 \cdot 4/7 = p^3 \cdot 4/7
|
18,132 |
|x| \geq |\Re{\left(x\right)}|\Longrightarrow |x|^2 - (\Re{(x)})^2 \geq 0
|
2,080 |
\cos^2(\pi/2 + n\cdot t) = \sin^2{n\cdot t}
|
32,701 |
-x_1\cdot 2 + 2 = x_1
|
-4,088 |
\dfrac{y^5}{y} = \dfrac{y \cdot y \cdot y \cdot y \cdot y}{y} = y^4
|
8,166 |
(x + k) * (x + k) = k * k + x * x + x*k*2
|
16,840 |
p^2\cdot \frac{1}{2}\cdot (p + (-1)) = \left(p^3 - p^2\right)/2
|
17,928 |
\tfrac{1}{c \cdot x} = \frac{1}{c \cdot x}
|
47,434 |
\frac{\sin(x)}{\cos(x)} + 1/\sin(x) = \dfrac{\sin^2\left(x\right) + \cos(x)}{\sin(x)\cdot \cos\left(x\right)}
|
15,742 |
n^{a}/n^{b} = 1/n^{b-a} \to 0
|
12,032 |
\left(y + \left(-1\right)\right)^{\frac{1}{2}} = (y + (-1))^{1/2} \neq (y + (-1))^{-1/2}
|
626 |
(E/x) * (E/x) = \frac{E}{x}*E/x
|
45,865 |
158 = 2*79
|
3,062 |
\left(a - b\right)^2 = (b - a)^2 = a^2 + b \cdot b - 2 \cdot a \cdot b
|
13,170 |
2^k - 2\times k + 2\times (-1) + 1 = 2^k - 2\times k + (-1)
|
24,701 |
2^2 - 2 \cdot k + k^2 = \left(k + (-1)\right) \cdot (k + 2 \cdot (-1)) + k + 2 = k^2 - 3 \cdot k + 2 + 2 + k = k^2 - 2 \cdot k + 4
|
-20,518 |
\dfrac{20 \cdot q}{q \cdot 90} = \tfrac{q \cdot 10}{10 \cdot q} \cdot \frac{1}{9} \cdot 2
|
8,062 |
\sin{3\times x}\times \cos{3\times x} = \frac12\times \sin{6\times x}
|
9,558 |
\alpha \cdot a = \alpha \cdot a
|
13,501 |
\pi*5/6*34 = \pi*\frac{85}{3}
|
7,063 |
\theta^{a + b} = \theta^a \theta^b
|
5,516 |
1 + ((-1) + x)\cdot (1 + x) = x^2
|
12,792 |
\left(z' + x'\right) \cdot \left(z' + x'\right) - (x' - z')^2 = 4 \cdot z' \cdot x'
|
16,198 |
(1 + x)^2 - x^2 = 2\times x + 1
|
-1,965 |
-3/4\cdot \pi + \dfrac{5}{12}\cdot \pi = -\pi/3
|
9,958 |
\sin(3*z) = \sin(2*z + z) = \sin(2*z)*\cos(z) + \cos(2*z)*\sin(z)
|
38,490 |
218^2 + (-1) = 219\times 217 = 3\times 73\times 7\times 31
|
19,624 |
(3^{1/6})^n = (1 + p)^n \geq 1 + n p
|
2,820 |
m\cdot 8 = m\cdot \left(5 + 3\right)
|
19,106 |
( G \cdot B \cdot f, e) = \left( B \cdot f, G \cdot e\right) = ( f, B \cdot G \cdot e)
|
6,209 |
\dfrac{1}{\ln(4)}\ln(2) = \frac12
|
-10,683 |
\frac{1}{5\cdot r}\cdot (2\cdot r + 8)\cdot 15/15 = \left(120 + 30\cdot r\right)/\left(75\cdot r\right)
|
-3,566 |
\frac{66}{88*x}*x^3 = \dfrac{1}{x}*x^3*66/88
|
-24,846 |
\int \frac{1}{y^6}\,\mathrm{d}y = \dfrac{1}{y^5\cdot (-6 + 1)} + C = -\dfrac{1}{5\cdot y^5} + C
|
-20,605 |
\frac{1}{-12*x + 28*(-1)}*(28*x + 4) = 4/4*\dfrac{7*x + 1}{-3*x + 7*(-1)}
|
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