id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-25,010
|
0.38 = \tfrac{1}{50}\cdot 19
|
25,658
|
E\cdot x/(E\cdot B) = \tan{B\cdot E\cdot x} \Rightarrow x\cdot E\cdot B = \arctan{E\cdot x/(B\cdot E)}
|
3,362
|
\sum_{k=0}^{m + 3*(-1)} 1 = \sum_{k=0 + 1}^{m + 3*(-1) + 1} 1 = \sum_{k=1}^{m + 2*\left(-1\right)} 1
|
5,004
|
(y + 5\cdot (-1))\cdot (y + 1) = y^2 - 4\cdot y + 5\cdot (-1)
|
24,332
|
(4g^2 + hg \cdot 4)/4 = \dfrac14(\left(g \cdot 2 + h\right)^2 - h^2)
|
30,862
|
m\times p + m\times n = m\times \left(p + n\right)
|
10,059
|
32\cdot 2/\left(72\cdot 2\right) = \dfrac{1}{72}\cdot 32
|
49,099
|
( 5, 4) + ( 2, 7) = \left( 5 + 2, 4 + 7\right) = \left[7, 11\right]
|
15,253
|
\frac{1}{y^2 + 1}\times \left(2\times y^2 + y\times |y| + 2\right) = \frac{3\times y^2 + 2}{y^2 + 1} = 3 - \frac{1}{y^2 + 1}
|
-734
|
e^{14 \times i \times \pi/4} = (e^{\frac{\pi}{4} \times i})^{14}
|
7,998
|
6!*2100*3! = 9072000
|
24,136
|
e^{i*x_k} = (-1)^k = e^{-i*x_k}
|
-20,118
|
\frac{72 \cdot (-1) + 18 \cdot x}{9 \cdot x + 90 \cdot \left(-1\right)} = \frac{1}{10 \cdot \left(-1\right) + x} \cdot \left(x \cdot 2 + 8 \cdot (-1)\right) \cdot \tfrac99
|
7,669
|
-\left(-t + m\right)\times 4 = (-m + t)\times 4
|
24,341
|
x^{j + (-1)} s j + r x^{\left(-1\right) + i} i = \frac{d}{dx} x^i r + s \frac{\partial}{\partial x} x^j
|
1,637
|
x + \alpha \cdot 3 = \alpha + \alpha + x + \alpha
|
26,898
|
\left(x * x + 13/25\right)*25 = 13 + x * x*25
|
44,891
|
\frac{1}{2} \cdot (3^k + (-1)) + 3^k = (3^k + (-1) + 2 \cdot 3^k)/2 = (3 \cdot 3^k + (-1))/2 = (3^{k + 1} + (-1))/2
|
-153
|
\frac{7!}{(7 + 3 \cdot \left(-1\right))! \cdot 3!} = \binom{7}{3}
|
38,179
|
e^{1/e} = e^{\tfrac1e}
|
126
|
\cos(\dfrac{\theta}{2}) = \sin(\theta)/(\sin(\theta/2)*2)
|
34,156
|
1 - \sin\left(\frac{\pi}{2} - x\right) = 1 - \cos{x} = 2 \cdot \sin^2{x/2}
|
-20,539
|
\dfrac{7 + q\cdot 7}{q + 1} = \frac{1 + q}{1 + q}\cdot 7/1
|
-25,051
|
\frac{4}{13} \cdot \frac{6}{12} = 24/156 = \dfrac{1}{13}2
|
17,881
|
\frac{1024}{3125} = (\tfrac{4}{5})^5
|
21,640
|
\frac{1}{4} + 1/4 = 1/2
|
14,585
|
\int e^d e^{-bd}\,\mathrm{d}d = \int e^{d - bd}\,\mathrm{d}d = \int e^{(1 - b) d}\,\mathrm{d}d
|
29,548
|
\left(-1\right) + 2^{1092} = \left(2^{273} + \left(-1\right)\right) \cdot (1 + 2^{546}) \cdot (2^{273} + 1)
|
2,696
|
d/dx \dfrac1x = -\dfrac{1}{x * x}*\frac{dx}{dx}
|
1,862
|
K + (-1) \leq -t + l \Rightarrow 1 + l \geq K + t
|
-3,359
|
\sqrt{150} + \sqrt{54} = \sqrt{9\cdot 6} + \sqrt{25\cdot 6}
|
27,679
|
2 = 4/2 = \tfrac{4}{4*\frac{1}{2}}
|
3,627
|
u \cdot G \cdot V + u_{s \cdot s} \cdot C \cdot x + u_s \cdot (G \cdot x + V \cdot C) = G \cdot u \cdot V + C \cdot u_{s \cdot s} \cdot x + C \cdot u_s \cdot V + G \cdot u_s \cdot x
|
-23,522
|
0.12 ^ 6 = (1 - 0.88)^6
|
-24,721
|
\frac{1}{16 \cdot (-1) + m^2} \cdot (2 \cdot m + 2 \cdot (-1)) + \frac{1}{m \cdot m + 16 \cdot (-1)} \cdot (6 - m) = \frac{1}{m^2 + 16 \cdot (-1)} \cdot (m + 4)
|
4,232
|
E[B]\cdot E[Q] = E[Q\cdot B]
|
29,246
|
h \cdot h - b \cdot b = (h - b) \cdot (h + b)
|
31,413
|
\sin{5t}=\sin{(4t+t)}
|
594
|
det\left(x*Y + F\right) = det\left(F + Y*x\right)
|
-7,904
|
\left(52 - 64 \cdot i + 39 \cdot i + 48\right)/25 = \left(100 - 25 \cdot i\right)/25 = 4 - i
|
6,404
|
x_g u_j = x_{i'} u_i \implies \frac{x_g u_j}{u_i} = x_{i'}
|
26,972
|
(z_2 + z_1)^2 = z_1 \cdot z_1 + z_1 \cdot z_2 \cdot 2 + z_2^2
|
27,595
|
\tfrac{30*\dfrac{6*10*1/60}{60}*20}{60} = 1/6
|
12,940
|
(b + i)^3 - b^3 = (b + 1 - b) ((b + 1)^2 + (b + 1) b + b^2) = 3 b b + 3 b + 1
|
8,828
|
4/5 \cdot \sqrt{r^2 + 9} = r \Rightarrow r = 4
|
813
|
1 - x^2 \cdot 2 - x = (1 - x \cdot 2) \cdot (x + 1)
|
12,928
|
700 \cdot (-1) + z \cdot z \cdot 4 + z \cdot 120 = 0 \implies (z + 35) \cdot (5 \cdot (-1) + z) = 0
|
20,030
|
\sin(\frac{\pi}{4}) = \cos(\frac{1}{4} \cdot \pi)
|
25,370
|
s^2 + 4*s + 5 = 1^2 + (s + 2)^2
|
7,249
|
17^5\times (13^2\times 3\times 7)^2 = 17^5\times 13^4\times 3^2\times 7^2
|
16,217
|
\sqrt{3} = -\tan(\frac{1}{12}\pi) + 2
|
25,679
|
(\left(-3\right)*\pi)/4 = -3*\pi/4
|
9,951
|
-a^3 + z^3 = (z - a) \cdot (z^2 + a \cdot z + a^2)
|
33,118
|
\left. \frac{\partial}{\partial i} \left(k\operatorname{im}{(T)}\right) \right|_{\substack{ i=i }} = \left. \frac{\partial}{\partial i} (\operatorname{im}{\left(TT\right)} k) \right|_{\substack{ i=i }}
|
-4,214
|
x\cdot \frac{1}{7}\cdot 8 = \frac{8\cdot x}{7}\cdot 1
|
-21,630
|
-1/2 = -\frac12
|
22,426
|
2*(y - 1/2) + 1 = 2*y
|
30,280
|
\dfrac{y*2 + (-1)}{y + (-1)} = \frac{2 - 1/y}{-1/y + 1}
|
18,663
|
\frac{1}{2}\cdot (2 + x^2 + x) = {x \choose 2} + {x \choose 0} + {x \choose 1}
|
2,138
|
\frac13 \cdot (1 + 2/3) = 5/9
|
270
|
n^2 - n + n + (-1) = (-1) + n * n
|
39,297
|
(10 + 6\left(-1\right))^n = 4^n \geq 2^n
|
6,343
|
B \cdot A + 0 = B \cdot A
|
27,207
|
\cos\left(x\right) = \cos(x) + 1 + \left(-1\right)
|
11,041
|
\frac{f}{c\cdot b^n} = \frac{b^{-n}\cdot f}{c}
|
13,287
|
\frac{1}{(-1) \cdot c} = -\dfrac{1}{c}
|
16,996
|
1 + 2^{546} = (2^{182} + 1) \cdot (2^{364} - 2^{182} + 1)
|
32,487
|
\dfrac{1}{2! \cdot 4! \cdot 1!} \cdot 7! = \binom{7}{2} \cdot 5
|
8,374
|
2 - b \cdot 2 \Rightarrow \left(1 - b\right) \cdot 2 = 0
|
-11,563
|
-4 + 15 \cdot (-1) + i \cdot 4 = -19 + 4 \cdot i
|
38,497
|
\frac{y}{1 + |y|} = \frac{1}{1 + y}y = 1 - \tfrac{1}{1 + y}
|
33,348
|
\cos{\varphi} = \cos{-\varphi}
|
14,035
|
2^{k + (-1)} + \left(-1\right) = \frac{1}{2} \cdot (2 \cdot \left(-1\right) + 2^k)
|
-9,272
|
-55\cdot y^2 = -5\cdot 11\cdot y\cdot y
|
23,671
|
18 = 2\cdot 1^2 + 4 \cdot 4
|
5,484
|
\frac{35}{12} = -\left(\frac{7}{2}\right)^2 + \dfrac{1}{6}*91
|
39,682
|
-3/9 \cdot \frac{5}{10} + 1 = 5/6
|
24,845
|
2^a\cdot 2^x = 2^{a + x}
|
-29,214
|
\left(-1\right) + 5\cdot 4 = 19
|
-20,056
|
\tfrac{1}{9}9 \frac{1}{k*(-9)}(1 + 5k) = (45 k + 9)/(k*\left(-81\right))
|
33,256
|
73 = 72\cdot \left(-1\right) + 145
|
277
|
\frac{y^2}{-\frac{1}{1 + y^2} + 1} = y^2 + 1
|
-18,309
|
\tfrac{k^2 - 7k}{k^2 - k\cdot 9 + 14} = \dfrac{k}{\left(2(-1) + k\right) (7\left(-1\right) + k)}(7(-1) + k)
|
9,153
|
R \cdot s' \cdot s \implies s' \cdot R \cdot s
|
-3,419
|
\sqrt{2} \cdot (1 + 3 + 2) = \sqrt{2} \cdot 6
|
-3,957
|
\dfrac{1}{k^3}*k * k = \frac{k*k}{k*k*k} = \dfrac{1}{k}
|
9,747
|
H*H^V = H^V*H
|
-7,073
|
3/14 = 3/7 \cdot 4/8
|
2,137
|
R_1 = q + (1 - q) \cdot (1 + R_1)\Longrightarrow R_1 = 1/q
|
264
|
(-1) + y^7 = (y + \left(-1\right)) \times (y^6 + y^5 + \dotsm + y + 1)
|
33,259
|
\frac{1}{\sqrt{2} + 2} + 1/(\sqrt{2}) = 1
|
-27,850
|
\frac{\text{d}}{\text{d}y} \csc(y) = -\cot\left(y\right)\cdot \csc(y)
|
-11,959
|
14/15 = \frac{1}{4\pi}x\cdot 4\pi = x
|
-25,865
|
\dfrac{1}{4^3} \cdot 4^8 = 4^5
|
10,048
|
b^2 + x * x + 2*x*b = \left(x + b\right)^2
|
11,306
|
15!/7! = \frac{1}{4!} \cdot 13!
|
-2,318
|
\frac{1}{17} = 2/17 - \frac{1}{17}
|
6,798
|
(2*(-1) + 1) * (2*(-1) + 1) = ((-1) + 2)^2
|
-3,963
|
\frac{1}{2 \cdot n^2 \cdot n} \cdot 5 = \frac{5 / 2}{n \cdot n \cdot n} \cdot 1
|
-10,431
|
\dfrac{1}{2} \cdot 2 \cdot \frac{2}{z + \left(-1\right)} = \frac{1}{2 \cdot (-1) + 2 \cdot z} \cdot 4
|
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