id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
14,443
|
202^3 - 171^3 = 3242197 = 85^2 * 85 + 138^3 = 76^3 + 141^3
|
-23,119
|
\frac{189}{64} = \frac{1}{16}\cdot 63\cdot 3/4
|
8,574
|
2*\gamma*z + \gamma^2 = -z^2 + (z + \gamma)^2
|
20,585
|
h * h + b * b = (40 - h - b)^2 = h^2 + b * b + 1600 - 80*(h + b) + 2*h*b
|
11,864
|
x^2 + 4 \cdot x + 8 = \left(x + 2\right)^2 + 4 = (x + 2)^2 + 13 \cdot \left(-1\right)
|
50,200
|
3*5*7*219091 = 23004555
|
45,375
|
2*60 - 119 = 1
|
-20,418
|
-2/5*\dfrac{1}{9}*9 = -\frac{18}{45}
|
-6,305
|
\tfrac{1}{(x + 9 \cdot (-1)) \cdot \left(x + 6\right)} = \dfrac{1}{54 \cdot (-1) + x^2 - 3 \cdot x}
|
-25,294
|
\frac{\mathrm{d}}{\mathrm{d}z} \frac{1}{z^6} = -\tfrac{1}{z^7}\cdot 6
|
1,344
|
4 + (s^2 + 2s + 1)\cdot 2 + s + 1 = 2s \cdot s + s\cdot 5 + 7
|
15,269
|
(z + g)*\left(z^2 - z*g + g^2\right) = z * z * z + g^3
|
23,079
|
5^2 \cdot 5 \cdot 4 \cdot 4 \cdot 3 = 6000
|
24,484
|
\left(c + x^2 \cdot a + b \cdot x\right) \cdot (x + 1) = c + a \cdot x^3 + (a + b) \cdot x^2 + (c + b) \cdot x
|
27,145
|
n^{\frac{3}{2}} \times 8 = (\sqrt{n} \times 2)^3
|
32,470
|
\left(-q + 1\right)/4 + q = \frac34 \cdot q + 1/4
|
-19,720
|
\tfrac{36}{7} \cdot 1 = \dfrac{36}{7}
|
-7,624
|
\dfrac{1 - 2\cdot i}{-2\cdot i + 1}\cdot \frac{-5\cdot i + 10}{1 + i\cdot 2} = \frac{1}{2\cdot i + 1}\cdot (10 - i\cdot 5)
|
33,386
|
h\cdot z\cdot H = h\cdot z\cdot H
|
-27,383
|
581 = 379\cdot (-1) + 960
|
-2,441
|
\sqrt{6} \cdot \left(4 + 3 (-1)\right) = \sqrt{6}
|
3,149
|
\cos(z + y) = -\sin\left(z\right) \cdot \sin(y) + \cos(y) \cdot \cos\left(z\right)
|
-2,975
|
8 \cdot \sqrt{7} = \sqrt{7} \cdot (5 + 3)
|
15,742
|
\tfrac{m^{h_1}}{m^{h_2}} = \frac{1}{m^{-h_1 + h_2}}
|
13,917
|
\dfrac{(n + 1)!}{2^{n + 1}} = \frac{n!}{2^n}\times \frac{1}{2}\times (n + 1) \gt \dfrac{n!}{2^n}
|
-2,363
|
\left(-2\right)^2 = (-2)*(-2) = 4
|
29,460
|
i = \cos(\pi/2) + i \times \sin(\pi/2) = e^{\dfrac{i}{2} \times \pi}
|
11,159
|
xx^{-i} zx^i = x^{-i} zx^i x
|
29,971
|
\frac14\cdot (b - h) + \frac{1}{4}\cdot 3\cdot (b - h) = b - h
|
13,464
|
\frac{1}{(-1) \times x^2} = -\dfrac{1}{x \times x} = -\frac{1}{x^2}
|
867
|
\frac{\partial}{\partial y} (\dfrac{1}{(2*k + 1)!}*y^{2*k + 1}) = y^{2*k}/(2*k)!
|
-3,328
|
\sqrt{6} \cdot 8 = \sqrt{6} \cdot (5 + 3)
|
-12,043
|
\frac{1}{24}\cdot 7 = s/(18\cdot \pi)\cdot 18\cdot \pi = s
|
16,385
|
\sin(c \cdot 2)/2 = \cos(c) \cdot \sin(c)
|
-5,108
|
10^{2 \cdot \left(-1\right) + 7} \cdot 0.13 = 10^5 \cdot 0.13
|
-27,389
|
2 + 988 = 990
|
-15,924
|
-44/10 = 10/10 - 6\cdot \frac{9}{10}
|
-2,777
|
\sqrt{10}*((-1) + 2 + 4) = \sqrt{10}*5
|
-11,471
|
i \cdot 7 + 6 + 20 = i \cdot 7 + 26
|
26,405
|
-5 \cdot \sqrt{3} = 9 - 5 \cdot \sqrt{3} + 9 \cdot (-1)
|
7,510
|
x^2 + \gamma \cdot \gamma + i^2 = 2 \cdot x \cdot \gamma \cdot i \Rightarrow x = \gamma = i = 0
|
26,788
|
1 = -2\times 3 + 7
|
3,628
|
\frac{2 \cdot 2}{2 + 9} = 4/11
|
-11,081
|
\left(x + 10 \cdot (-1)\right)^2 + A = (x + 10 \cdot \left(-1\right)) \cdot (x + 10 \cdot (-1)) + A = x \cdot x - 20 \cdot x + 100 + A
|
23,203
|
\mathbb{E}[R^2 - 2\cdot R\cdot \mathbb{E}[R] + \mathbb{E}[R]^2] = \mathbb{E}[R^2] - 2\cdot \mathbb{E}[R]^2 + \mathbb{E}[R] \cdot \mathbb{E}[R] = \mathbb{E}[R \cdot R] - \mathbb{E}[R]^2
|
15,088
|
2^4 \cdot 5^2 = \left(2^2 \cdot 5\right)^2
|
-16,364
|
\left(4*13\right)^{1/2}*3 = 3*52^{1/2}
|
7,330
|
\cos(π/4) - \dfrac{π}{4\cdot \sin\left(\dfrac{1}{4}\cdot π\right)} = \frac{\sqrt{2}}{2\cdot \left(1 - \dfrac{π}{4}\right)} \gt 0
|
10,827
|
3 (-1) + y*2 = y - -y + 3
|
-26,135
|
7 \times (e^7 - \dfrac{1}{e^{14}}) = -\frac{1}{e^{14}} \times 7 + 7 \times e^7
|
7,943
|
-y \gt 0 \implies y \lt 0
|
14,379
|
\frac{1}{9}\cdot \left(2\cdot n + 5\cdot (-1)\right) = (2\cdot n + 5\cdot (-1))/9 = \dfrac{n}{9}\cdot 2 - 5/9
|
-18,732
|
0.6915 - 0.4013 = 0.2902
|
-20,796
|
\frac{1}{5} \cdot 5 \cdot \left(-\frac{3}{9 + a \cdot 4}\right) = -\frac{15}{20 \cdot a + 45}
|
5,880
|
x*X = f \implies f/X = x
|
-19,505
|
\frac{5}{\frac{1}{2}} \cdot \frac16 = 5/6 \cdot 2/1
|
-1,064
|
3 \cdot 1/4/(1/8) = 3/4 \cdot \frac{8}{1}
|
26,984
|
N^2 = N \cdot N
|
-17,145
|
8 = 8 \cdot (-3 \cdot x) + 8 \cdot (-8) = -24 \cdot x - 64 = -24 \cdot x + 64 \cdot (-1)
|
13,717
|
-(-x^a + 1) + 1 - x^b = -x^b + x^a
|
19,684
|
\dfrac{3}{2}\frac{1}{3} = \frac{1}{2}
|
-13,923
|
\dfrac{1}{9 + 3 \cdot (-1)} \cdot 6 = 6/6 = 6/6 = 1
|
25,488
|
b_k * b_k + (-1) = (b_k + 1)*(b_k + (-1))
|
-2,676
|
((-1) + 5 + 2) \sqrt{5} = \sqrt{5}*6
|
7,945
|
\frac{x_n^n}{x_n} = x_n^{(-1) + n}
|
-23,540
|
1 - \frac{3}{7} = \frac174
|
28,869
|
\sum_{n=1}^∞ \sin\left(n\right) = \sin(1) + \sin(2) + \sin(3) + ... + \sin(n)
|
13,738
|
\left(2/3\right)^3 + \left(1/3\right) \cdot \left(1/3\right) \cdot \left(1/3\right) = 1/3
|
19,649
|
\frac12(\left(-2\right) \tfrac{1}{x^2 + (-1)}) = -\frac{1}{x^2 + (-1)} = \frac{1}{1 - x \cdot x}
|
20,202
|
\frac{1.8 - 3.8}{2 - 1.2} = -\frac{2}{0.8} = -\dfrac52
|
726
|
(1 + 1/n)^{n + 1} = (\frac1n \cdot \left(1 + n\right))^{n + 1}
|
-11,730
|
(\dfrac{1}{4}\cdot 3)^3 = \frac{1}{64}\cdot 27
|
14,852
|
h + f + g + e = 0 \Rightarrow -e - f - g = h
|
-29,400
|
7/4\cdot \frac{1}{3}\cdot 7 = \dfrac{7\cdot 7}{4\cdot 3} = \frac{49}{12}
|
-8,061
|
\frac{26 + 7\cdot i}{-i\cdot 5 - 2} = \frac{26 + i\cdot 7}{-2 - 5\cdot i}\cdot \frac{-2 + i\cdot 5}{-2 + 5\cdot i}
|
13,976
|
((-1) + n) \cdot (1 + n) \cdot n \cdot \dotsm \cdot 2 = (n + 1)!
|
-20,578
|
4/4\times \frac{1}{3\times (-1) + k}\times (-k + 9\times (-1)) = \dfrac{1}{k\times 4 + 12\times (-1)}\times (-k\times 4 + 36\times (-1))
|
2,785
|
\pi \cdot r^2 \cdot 9 - 4 \cdot r^2 \cdot \pi = 5 \cdot \pi \cdot r^2
|
-4,154
|
\dfrac{x^5\cdot 9}{54\cdot x^2 \cdot x}\cdot 1 = 9/54\cdot \frac{1}{x^3}\cdot x^5
|
-19,712
|
7\cdot 4/(5) = 28/5
|
2,537
|
0.5 + 0.5\times p\times 0.5 = p\Longrightarrow p = 2/3
|
-15,426
|
\frac{1}{(\frac{y^2}{q})^2}\cdot y^3 = \dfrac{1}{y^4\cdot \frac{1}{q^2}}\cdot y^3
|
11,805
|
\frac{2 \cdot \tan(x/2)}{\tan^2(\dfrac12 \cdot x) + 1} = \sin(x)
|
17,123
|
5/6 - \frac{1}{5} = 19/30
|
38,267
|
\frac{3!}{(3 + 2*\left(-1\right))!} = 6
|
6,950
|
(10 \cdot a + b) \cdot (10 \cdot a + b) = 100 \cdot a^2 + 20 \cdot a \cdot b + b \cdot b = 10 \cdot (10 \cdot a^2 + 2 \cdot a \cdot b) + b^2
|
33,108
|
612 = y^2 - (c + (-1))^2 = y + c + \left(-1\right)
|
-20,020
|
\frac{1}{14}*4 = 2/2*\frac27
|
37,712
|
7^{94} = 7^2 * 7*7^{91}
|
5,480
|
\frac{1}{2} \cdot (1 + \pi) = \frac{1}{2} + \frac{1}{2} \cdot \pi
|
22,041
|
-x\cdot 2 = -x - x
|
12,945
|
1/2 + 5^{\tfrac{1}{2}}/2 = (1 + 5^{1 / 2})/2
|
35,035
|
|-t\cdot 2 + 16| = 5\Longrightarrow 5.5 = t,10.5
|
12,910
|
(\gamma + 2 \cdot (-1))^2 + (\gamma \cdot \gamma - \frac{1}{2})^2 = \gamma^2 - 4 \cdot \gamma + 4 + \gamma^4 - \gamma^2 + 1/4 = \gamma^4 - 4 \cdot \gamma + 17/4
|
4,571
|
A' \cap ((A' \cap W) \cup (B' \cap W)) = (A' \cap W) \cup (W \cap (A' \cap B'))
|
-1,977
|
\frac{7}{4}\cdot \pi + 7/6\cdot \pi = \dfrac{1}{12}\cdot 35\cdot \pi
|
3,017
|
\cos^4{x} = \left(\cos^2{x}\right)^2 = \frac{1}{4}(1 + 2\cos{2x} + \cos^2{2x})
|
31,038
|
\frac{1}{1 + z^2} = \frac{1}{(1 + z + (-1) + 1) * (1 + z + (-1) + 1)} = \frac{1}{1 + 1 + (z + \left(-1\right))^2 + 2*(z + \left(-1\right))}
|
27,746
|
\left(z + (-1)\right) * \left(z + (-1)\right) = z*z - z - z - -1 = z^2 - 2*z + 1
|
6,551
|
500 + 334 + 200 + 167\cdot (-1) + 100\cdot \left(-1\right) + 67\cdot (-1) + 34 = 734
|
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