id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
14,214
|
7290 = 1 \times 9 \times 9 \times 9 \times 5 \times 2
|
13,211
|
30 = (63 - 30 \cdot q) \cdot q + (63 - 30 \cdot q) \cdot q \cdot q \cdot q = 63 \cdot q - 30 \cdot q^2 + 63 \cdot q \cdot q \cdot q - 30 \cdot q^4
|
16,455
|
\mathbb{E}[\left(Z_1 \cdot Z_2\right)^2] = \mathbb{E}[Z_1^2 \cdot Z_2^2] = \mathbb{E}[Z_1 \cdot Z_1] \cdot \mathbb{E}[Z_2 \cdot Z_2]
|
-25,219
|
\frac{\mathrm{d}}{\mathrm{d}y} y^m = y^{(-1) + m} \cdot m
|
-22,221
|
\eta \cdot \eta + \eta\cdot 5 + 6\cdot (-1) = \left((-1) + \eta\right)\cdot (\eta + 6)
|
6,835
|
1 - 80 \times x^2 - x \times 120 + 45 \times (-1) = 1 - 5 \times \left(9 + x^2 \times 16 + x \times 24\right)
|
25,464
|
\tfrac{1}{n \cdot n + 4\cdot (-1)}\cdot 4 = \tfrac{1}{(n + 2)\cdot (n + 2\cdot (-1))}\cdot (n + 2 - n + 2\cdot \left(-1\right)) = \frac{1}{n + 2\cdot (-1)} - \dfrac{1}{n + 2}
|
2,132
|
\frac{16}{27} = \frac{2^4}{3^4} + \frac{1}{3^4} \cdot 2^3 \cdot 4
|
-30,713
|
x*20 + 5*(-1) = ((-1) + 4*x)*5
|
47,113
|
6^{65} = 3^{65}\cdot 2^{65}
|
16,614
|
(2 + k)/k = \left(1 + k\right)/k \dfrac{1}{k + 1}(k + 2)
|
11,570
|
7^{2l} + 208 l + \left(-1\right) = 48^2 c + 256 l = 256*(9c + l)
|
5,386
|
15/79 = 0.189873 \cdot \ldots \approx 0.19
|
21,012
|
(f \cdot z)^2 = (z \cdot f) \cdot (z \cdot f)
|
41,794
|
1 = 0.999 \times \cdots
|
525
|
\left(\left(0 = \|x\|_0 \Rightarrow \|\mathbb{P}(x)\|_2 = 0\right) \Rightarrow 0 = \mathbb{P}(x)\right) \Rightarrow 0 = x
|
-26,652
|
(p^4*9 + 10) (9p^4 + 10 (-1)) = 81 p^8 + 100 (-1)
|
11,058
|
\left(m + (-1)\right)/m = 1 - \frac1m
|
-1,756
|
π \cdot \frac{1}{12} \cdot 5 + π = \dfrac{1}{12} \cdot 17 \cdot π
|
14,477
|
z = 5 \Rightarrow z^2 = 25
|
1,268
|
(x^2 + k \cdot k)^2 - (x^2 - k^2) \cdot (x^2 - k^2) = (2 \cdot x \cdot k)^2 = 2 \cdot 2 \cdot x \cdot x \cdot k \cdot k
|
-25,273
|
\frac{\mathrm{d}}{\mathrm{d}y} \frac{1}{y^3} = -\frac{3}{y^4}
|
23,115
|
x \cdot x\cdot 2 - x\cdot 3 = 2((-1) + x^2) - 3(1 + x) + 5
|
3,181
|
k^9 - k^3 = (\left(-1\right) + k^3) k^3 \cdot \left(k \cdot k \cdot k + 1\right)
|
18,431
|
\left(6l + 3\cdot (2x + 1) = 9 = 6(l + x) + 3 \Rightarrow x + l = 1\right) \Rightarrow l = 1 - x
|
-1,717
|
\pi/6 - \pi/12 = \pi/12
|
23,098
|
\tfrac{1}{\frac1a + \frac1b} = a*\dfrac{b}{b + a}
|
7,388
|
-16 = \left(5 + 7*\left(-1\right)\right)*\left(5 + 3\right)
|
32,768
|
\dfrac{t^2+x^2-tx}{tx} = \dfrac76 \implies 6t^2-13tx+6x^2 = 0 \implies 6t^2 - 9tx - 4tx + 6x^2 = 0
|
-20,342
|
\frac33 \cdot \frac{(-2) \cdot i}{-3 \cdot i + 3 \cdot (-1)} = \dfrac{i \cdot (-6)}{-9 \cdot i + 9 \cdot \left(-1\right)}
|
15,191
|
1/(x b) = \dfrac{1}{x b} = x b^2
|
-23,551
|
\frac{3}{16} = \frac{\dfrac{1}{8}*3}{2}
|
-9,484
|
36\cdot (-1) + k\cdot 84 = 2\cdot 2\cdot 3\cdot 7\cdot k - 2\cdot 2\cdot 3\cdot 3
|
-13,922
|
\frac{42}{8 + 6} = \dfrac{42}{14} = \frac{42}{14} = 3
|
15,320
|
\frac{\frac{1}{k^3} \cdot \frac{1}{x^2}}{\frac{1}{k^5} \cdot x^6} \cdot 1 = \frac{k^5}{k^3 \cdot x^6 \cdot x^2} = \frac{k^2}{x^8}
|
-21,028
|
-\frac157 \dfrac{1}{x + 4}(4 + x) = \frac{1}{x*5 + 20}(28 (-1) - x*7)
|
25,270
|
CD^2 = CD^2
|
4,944
|
c\cdot c\cdot c\cdot c\cdot c\cdot c = (c\cdot c\cdot c)^2
|
12,632
|
\sin(z*2) = 2\cos\left(z\right) \sin\left(z\right)
|
20,324
|
WS = SW
|
22,189
|
(1/x + 1 + x)^2 = x^2 + x\cdot 2 + 3 + 2/x + \frac{1}{x \cdot x}
|
115
|
34/49 - \frac{18}{49} = \frac{16}{49}
|
-17,987
|
5 \cdot (-1) + 75 = 70
|
13,853
|
4 \cdot k \cdot k + 4 \cdot k + 1 = 1 + 4 \cdot \left(k^2 + k\right)
|
-7,820
|
(20 - 40 i + 15 i + 30)/25 = \dfrac{1}{25}(50 - 25 i) = 2 - i
|
3,598
|
-\tfrac{1}{x} = \frac{1}{x \cdot x}\cdot (x\cdot \left(-1\right))
|
927
|
10 + 6 \cdot i + (z - 3 \cdot i)^2 = 10 + 6 \cdot i + z^2 - 6 \cdot i + 9 \cdot (-1) = 1 + z \cdot z
|
54,425
|
1597 = 610 + 987
|
5,913
|
\left(Fy = \lambda y \Rightarrow Fy \lambda = F^2 y\right) \Rightarrow Fy = \lambda Fy = \lambda * \lambda y
|
40,739
|
2^{\frac14} = 2^{\dfrac{1}{4}}
|
-17,718
|
3 = 23 + 20 (-1)
|
-5,082
|
18.0 \cdot 10^2 \cdot 10 = 10^{1 + 2} \cdot 18
|
13,514
|
(t-2)^2 = t^2 - 4t + 4
|
32,761
|
\dfrac{1}{(-1)\cdot g} = -\tfrac1g
|
17,345
|
2/3 + 2 = 8/3
|
28,132
|
-V^2 + (V + C) * (V + C) - C^2 = C*V + V*C
|
16,085
|
b + a = a + b \Rightarrow [a, b]
|
15,712
|
n*4 + 2 = \left(2n + 1\right)*2
|
3,627
|
x\cdot u_{q\cdot q}\cdot C + (x\cdot G + C\cdot W)\cdot u_q + G\cdot u\cdot W = u_{q\cdot q}\cdot C\cdot x + W\cdot u_q\cdot C + x\cdot u_q\cdot G + W\cdot u\cdot G
|
1,053
|
z^2 + y \cdot y + y\cdot z\cdot 2 = \left(y + z\right)^2
|
33,788
|
e \cdot G = e \cdot G
|
5,935
|
y^3 \cdot z \cdot z \cdot z = (z \cdot y)^3
|
25,907
|
\left\lfloor{(a + b + \left(-1\right))/b}\right\rfloor = \left\lfloor{((-1) + b)/b + \frac{a}{b}}\right\rfloor
|
492
|
-2\cdot a = \frac{1}{-a - 1}\cdot (-b + 7) \Rightarrow 7 - b = a\cdot 2 + 2\cdot a^2
|
22,321
|
1 = 111 \cdot \dots
|
13,192
|
(n + 1)! + n! = \left(1 + n\right)\cdot n! + n!
|
36,896
|
X + E = E + X
|
-26,546
|
1^2 + 2 \cdot y + y^2 = 1 + y \cdot 2 + y \cdot y
|
-3,065
|
\sqrt{7} \cdot \sqrt{16} + \sqrt{25} \cdot \sqrt{7} = 4 \cdot \sqrt{7} + 5 \cdot \sqrt{7}
|
-21,613
|
1 = \cos\left(2 \cdot \pi\right)
|
-2,660
|
\sqrt{11} + 4 \cdot \sqrt{11} = \sqrt{11} \cdot \sqrt{16} + \sqrt{11}
|
33,591
|
3\cdot 4 + 3\cdot 3 = \left(3 + 4\right)\cdot 3
|
7,020
|
z \cdot z^2 + 8 \cdot (-1) = z^3 - z \cdot z \cdot 2 + z \cdot z \cdot 2 - z \cdot 4 + z \cdot 4 + 8 \cdot (-1)
|
5,589
|
\tfrac{17.4}{4} = 1/2\cdot \frac12\cdot 17.4
|
25,038
|
\dfrac{1}{g\cdot h} = \frac{1}{g\cdot h}
|
-15,957
|
-\frac{4}{10}\cdot 8 + 6/10\cdot 9 = \frac{1}{10}\cdot 22
|
-24,926
|
\sin(z) \cdot \cos(z) \cdot 2 = \sin\left(z \cdot 2\right)
|
31,027
|
3 \cdot m + 2 = n \implies \frac{n \cdot n}{3} \cdot 1 = 3 \cdot m^2 + m \cdot 4 + 1
|
26,063
|
n \cdot n \cdot n \cdot n \cdot n \cdot n \cdot n \cdot n = n^8
|
-15,212
|
\frac{1}{m^{16} \cdot \frac{1}{m^5 \cdot r^5}} = \dfrac{1}{\frac{1}{r^5 \cdot m^5} \cdot m^{16}}
|
-12,905
|
16 + 6\cdot (-1) = 10
|
25,512
|
d/dy \ln(y) = \dfrac{1}{e^{\ln(y)}} = \frac{1}{y}
|
9,864
|
m_1\cdot x - m_2\cdot x = (-m_2 + m_1)\cdot x
|
40,712
|
\tan\left(\theta\right) = \sin(\theta)/\cos\left(\theta\right)
|
17,626
|
x\cdot Y = x\cdot Y\cdot (A + Z') = x\cdot Y\cdot A + x\cdot Y\cdot Z'
|
-20,407
|
\frac{1}{p \cdot (-6)} \cdot (3 - p \cdot 10) \cdot \frac14 \cdot 4 = \frac{-p \cdot 40 + 12}{p \cdot \left(-24\right)}
|
36,464
|
\cos(22) \cdot \cos(38) - \sin(22) \cdot \sin(38) = \cos(22 + 38) = \cos(60) = \frac{1}{2}
|
16,186
|
\left(-C = -R + K \cdot R \implies R \cdot (-d \cdot I + K) = -C\right) \implies R = \dfrac{C \cdot (-1)}{-I \cdot d + K}
|
4,714
|
h = ( h, h\times 2, \dotsm)
|
13,662
|
c\cdot m\cdot \dfrac{1}{\xi}\cdot B = c\cdot B\cdot m/\xi
|
30,639
|
a^n \times a^x = a^{n + x}
|
25,029
|
\sum_{j_1=0}^{j_2 + 1 + (-1)} x^{j_1} = \sum_{j_1=0}^{j_2} x^{j_1}
|
2,677
|
x a^i = x a^i
|
-20,788
|
-\frac15*7*\frac{1 + l}{1 + l} = \frac{-7*l + 7*(-1)}{5 + 5*l}
|
-26,462
|
(-b + g)^2 = g^2 - 2 g b + b b
|
22,820
|
\tfrac{1}{2} = e^{-\log_e(2)}
|
-15,121
|
\dfrac{1}{m^{12}*\tfrac{m^5}{t^{20}}} = \dfrac{(\frac{1}{m^4})^3}{(\tfrac{m}{t^4})^5}
|
-13,131
|
62 \cdot \frac{1}{-5}/(-4) = \frac{62}{\left(-5\right) \cdot \left(-4\right)} = \frac{1}{20} \cdot 62
|
-5,025
|
53.2/1000 = \tfrac{1}{1000} \times 53.2
|
16,651
|
\sqrt{2} = -\sin(((-1) \pi)/4) + \sin\left(\pi/4\right)
|
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