id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-9,409 |
-q \times 2 \times 2 \times 3 \times 3 - 2 \times 2 \times 2 \times 3 = -q \times 36 + 24 \times (-1)
|
105 |
(B + H_2)/(H_1) = B/(H_1) + H_2/(H_1)
|
3,279 |
1 + 2^0 + 2^1\cdot \cdots\cdot 2^{(-1) + l} = 2^l
|
1,680 |
4 \cdot \cot(\theta) = \sqrt{3} \cdot (\cot^2(\theta) + 1) = \sqrt{3} \cdot \csc^2(\theta)
|
1,388 |
z \cdot 0 + 0 \cdot z^2 + 0 \cdot z^2 \cdot z + \dotsm + 0 \cdot z^{n + (-1)} + z^n = \dfrac{1}{(-1) + z} \cdot (z^{n + 1} - z^n)
|
25,013 |
(\vartheta^2 + a^2)^{\frac{1}{2}} = \sqrt{a^2 + \vartheta^2}
|
5,498 |
-\frac{1}{3}\cdot t + t = t\cdot 2/3
|
-9,274 |
3 \cdot q^3 + 21 \cdot q^2 = 3 \cdot 7 \cdot q \cdot q + q \cdot q \cdot 3 \cdot q
|
-30,925 |
32 = 48 - 8\cdot 2
|
-6,624 |
\frac{2}{n^2 + 5\cdot n + 4} = \frac{2}{(n + 4)\cdot \left(1 + n\right)}
|
-1,201 |
-21/24 = \tfrac{1}{24 \cdot \frac13} \cdot ((-21) \cdot 1/3) = -7/8
|
10,102 |
\cos\left(r\right) = \sin(-r + \dfrac{π}{2})
|
24,110 |
\int \frac{1}{y^2}\,\mathrm{d}y = \int \frac{1}{y \cdot y}\,\mathrm{d}y = -1/y
|
14,611 |
\Z_{24} = \left\{23, 2, \cdots, 1, 3\right\}
|
33,030 |
0 = \tan^{-1}{\dfrac{0}{\sqrt{2}}}
|
25,177 |
(g\cdot d)^2 = g^2\cdot d^2
|
2,214 |
\sin(\frac{π}{4}) = \cos(\frac14\cdot π) = \sqrt{2}/2
|
6,507 |
3 \cdot x^3 + 4 \cdot (-1) = 3 \cdot (x^3 - 4/3) = 3 \cdot \left(x - (\dfrac{4}{3})^{1/3}\right) \cdot (x^2 + \left(\dfrac43\right)^{\dfrac{1}{3}} \cdot x + (4/3)^{2/3})
|
22,485 |
89 + (1 + 2*(-1) + 3 + 4*\left(-1\right) + 5)*6 + 7*(-1) = 100
|
39,504 |
(-1) + n = k \implies 1 + k = n
|
-18,432 |
\dfrac{1}{\left(n + 8\cdot (-1)\right)\cdot n}\cdot \left(10 + n\right)\cdot \left(8\cdot (-1) + n\right) = \frac{1}{-8\cdot n + n^2}\cdot (n^2 + 2\cdot n + 80\cdot (-1))
|
-6,761 |
7 \cdot 9 \cdot 5 = 315
|
7,648 |
\sqrt{(g + h)^2} = |g + h| = \sqrt{g^2} + \sqrt{h^2}
|
513 |
-\tfrac12\cdot ((-1)\cdot \sqrt{-x^2 + 4}) + 2 = 2 + \sqrt{-x^2 + 4}/2
|
34,579 |
(f\cdot b)^i = (b\cdot f)^i
|
-11,572 |
-37 \cdot i + 15 + 20 \cdot (-1) = -5 - 37 \cdot i
|
-11,567 |
-3 i - 1 + 10 (-1) = -11 - 3 i
|
4,847 |
x^2 = \dfrac12\cdot (3 + \sqrt{5}) = x + 1
|
29,074 |
\sin{A*2} = \cos{A}*\sin{A}*2
|
19,489 |
E_2 = E_2 \cap (H \cup E_1) = (H \cap E_2) \cup (E_1 \cap E_2)
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16,071 |
\frac{1}{4} + \dfrac14\cdot 2 = \dfrac34 \lt 1
|
4,757 |
-b^4 + a^4 = (b + a) (a^2 + b^2) (a - b)
|
38,870 |
4!/2! \cdot 3 = 36
|
-12,937 |
\frac{3}{21} = \dfrac{1}{7}
|
393 |
\mathbb{Var}[x - Q] = \mathbb{E}[(x - Q) \cdot (x - Q)] - \mathbb{E}[x - Q]^2 = \mathbb{E}[x^2] - 2\cdot \mathbb{E}[x\cdot Q] + \mathbb{E}[Q^2] - (\mathbb{E}[x] - \mathbb{E}[Q])^2
|
-6,294 |
\dfrac{1}{a^2 - a\cdot 14 + 45}\cdot 2 = \frac{2}{(a + 9\cdot (-1))\cdot (a + 5\cdot \left(-1\right))}
|
20,076 |
a^y \times a^x = a^{x + y}
|
-17,665 |
66 + 2 \cdot \left(-1\right) = 64
|
-10,696 |
\dfrac{4\cdot y + 18\cdot (-1)}{18 + y\cdot 30} = \frac22\cdot \frac{y\cdot 2 + 9\cdot \left(-1\right)}{15\cdot y + 9}
|
-4,490 |
\frac{x + 17 (-1)}{3(-1) + x^2 + x \cdot 2} = -\frac{1}{x + (-1)}4 + \frac{5}{3 + x}
|
21,946 |
a^2 = b^2 rightarrow a = b
|
-10,740 |
\dfrac{1}{k + 3} \cdot (9 \cdot (-1) + k \cdot 2) \cdot \dfrac44 = \frac{8 \cdot k + 36 \cdot (-1)}{4 \cdot k + 12}
|
13,924 |
4(m + 1) \cdot (m + 1) + 1 = 4m^2 + 8m + 4 + 1 = 4m \cdot m + 1 + 8m + 4 < 3 \cdot 2^m + 8m + 4
|
309 |
9 \cdot x^2 + (-1) = (3 \cdot x)^2 - 1^2 = \left(3 \cdot x + (-1)\right) \cdot (3 \cdot x + 1)
|
3,471 |
x_1/\left(d_1\right) + x_2/(d_2) = \dfrac{1}{d_2\cdot d_1}\cdot (d_2\cdot x_1 + x_2\cdot d_1)
|
11,428 |
a_n \cdot b \cdot c = b \cdot c \cdot a_n
|
23,741 |
\left(c^3 + 9 \cdot (-1) = 0 \Rightarrow c \cdot c \cdot c = 9\right) \Rightarrow |9| = |c \cdot c^2|
|
22,473 |
-\frac{3 \cdot x + 4 \cdot y}{5 \cdot z - 8 \cdot w} = \frac{3 \cdot x + 4 \cdot y}{\left(-1\right) \cdot (5 \cdot z - 8 \cdot w)} = \frac{1}{-5 \cdot z + 8 \cdot w} \cdot \left(3 \cdot x + 4 \cdot y\right)
|
16,770 |
60 + 1 + (53 + 6 + 18 + 36)*2 = 287
|
19,869 |
\sqrt{1 - l_r^2} = l_r
|
2,442 |
\xi^6 + \alpha^6 = \xi \cdot \xi \cdot \xi \cdot \xi \cdot \xi \cdot \xi + (\alpha^2)^3 = \left(\xi \cdot \xi + \alpha^2\right) (\xi^4 - \xi^2 \alpha^2 + \alpha^4)
|
20,078 |
|e^{i\cdot q} + (-1)|^2 = |\cos\left(q\right) + (-1) + i\cdot \sin\left(q\right)|^2 = (\cos(q) + (-1))^2 + \sin^2(q)
|
28,227 |
\dfrac{n + 1}{2\cdot (-1) + n} = 1 + \dfrac{3}{n + 2\cdot (-1)}
|
11,068 |
1/2 \cdot (90 + 60 (-1)) = 15
|
-2,158 |
5/3 \pi = \pi \frac43 + \pi/3
|
21,130 |
\tan(u) = \frac{\sin(u)}{\cos\left(u\right)}
|
-17,094 |
-5\cdot p = -5\cdot p\cdot 5\cdot p + -5\cdot p\cdot (-2) = -25\cdot p^2 + 10\cdot p = -25\cdot p \cdot p + 10\cdot p
|
3,302 |
( 4, -2, 1) = \left( \dfrac12\cdot 8, -\frac{1}{2}\cdot 2^2, 2^3/8\right)
|
10,801 |
\dfrac{2\cdot π}{6} = \frac{π}{3}
|
7,453 |
x \times y^2 \times 3 + x^3 + y \times y \times y + 3 \times y \times x^2 = (x + y)^3
|
-29,512 |
60 = \dfrac{1}{(3 \cdot (-1) + 5)!} \cdot 5!
|
29,057 |
m = m \cdot (3 + 2 (-1)) = 3 m - 2 m = 3 m + 2 (-m)
|
-3,790 |
\frac{20*x^4}{12*x} = 20/12*\dfrac{x^4}{x}
|
15,526 |
x^3\cdot 4 - f^3 = 2 + 2\cdot f\cdot x
|
-20,366 |
\dfrac{9*q + 6}{q*45 + 30} = \frac15*1
|
13,037 |
-b^2 + d^2 = (b + d) \cdot (-b + d)
|
-1,628 |
-\frac{1}{4}3 \pi + 2\pi = \pi \dfrac{5}{4}
|
2,127 |
2/1 = 2 + \frac{1}{1} 0
|
24,151 |
E[\min{X, -Z + X}] = \min{E[X]\wedge E[X - Z]}
|
10,686 |
d/dz \csc^2(z*4) = d/dz \csc^2(z*4)
|
-20,011 |
\frac{1}{j*24 + 40}(-j*80 + 72 \left(-1\right)) = 8/8 \frac{-j*10 + 9(-1)}{j*3 + 5}
|
15,942 |
\dfrac{1}{21} \cdot 17 + 12/42 = \frac{17}{21} + \tfrac{6}{21} = 23/21
|
32,892 |
1/(-1) + \frac22 + 3/(-3) + \frac14\cdot 4 + 5/(-5) + \frac{6}{6} + \frac77 = 1
|
21,729 |
(l + 1)^3 = (1 + l) \cdot (1 + l) \cdot (1 + l)
|
17,348 |
(1 + l)! = \left(l + 1\right) \cdot l \cdot (l + \left(-1\right)) \cdot (l + 2 \cdot (-1)) \cdot \ldots \cdot 2
|
19,073 |
(c - f)^2 = f \cdot f + c^2 - f \cdot c \cdot 2
|
-18,327 |
\frac{1}{p^2 - 5 \cdot p} \cdot (30 \cdot (-1) + p^2 + p) = \dfrac{(6 + p) \cdot \left(5 \cdot (-1) + p\right)}{p \cdot (p + 5 \cdot (-1))}
|
8,471 |
-(A \cdot A - x \cdot x)^{3/2}/3 + C = C - \frac{1}{3} \cdot (A^2 - x^2)^{3/2}
|
-29,020 |
t^l\cdot t^m = t^{m + l}
|
26,322 |
12.121 = 10^4*0.001212*\cdots
|
-7,102 |
\frac{1}{22}5 = 6/12 \cdot \frac{5}{11}
|
2,168 |
\sin^2(x\cdot \sin^2(x)) = (\sin^2(x))^2 = \sin^4(x)
|
5,803 |
( z^2, z\cdot y) = z \cap ( z, y)^2 = z \cap ( z \cdot z, y)
|
19,769 |
10^0*3 + 10^1*2 + 10^2 = 123
|
15,015 |
\mathbb{N} := \left\{1, \ldots, 2, 0\right\}
|
20,923 |
2 \cdot \sin\left(5 \cdot y\right) \cdot \cos(4 \cdot y) = \sin(5 \cdot y + 4 \cdot y) + \sin(5 \cdot y - 4 \cdot y) = \sin(9 \cdot y) + \sin(y)
|
31,646 |
a^3 + b^3 + c^3 - bc a\cdot 3 = (c + a + b) \left(-ca + a^2 + b^2 + c^2 - ab - bc\right)
|
-11,504 |
i\cdot 5 - 5 = -5 + 0\cdot (-1) + 5\cdot i
|
-18,291 |
\frac{54 + z^2 + 15 \cdot z}{81 \cdot \left(-1\right) + z^2} = \frac{(9 + z) \cdot (6 + z)}{(9 \cdot \left(-1\right) + z) \cdot (z + 9)}
|
22,710 |
\dfrac16 = 1/10 + 1/15
|
3,991 |
\overline{n + l} = \overline{l} + \overline{n}
|
14,505 |
216 = 6 \cdot 6 \cdot 6 = 2^2 \cdot 2\cdot 3^3
|
20,724 |
\frac 12 \cdot(90-60) = 15
|
15,069 |
\left\lfloor{\frac15 \cdot 47}\right\rfloor = 9
|
4,354 |
\frac{c}{d} = \dfrac{1}{d}\cdot c
|
43,534 |
3^2 \cdot 13 = 117
|
16,996 |
(2^{364} - 2^{182} + 1)\cdot (1 + 2^{182}) = 2^{546} + 1
|
20,917 |
\cos{c} \cos{g} - \sin{g} \sin{c} = \cos\left(g + c\right)
|
3,512 |
2\cdot 1/3/2 + 1/(2\cdot 3) = 1/2
|
3,637 |
((x + 1)^2 - x^2)/x = (x^2 + 2\cdot x + 1 - x \cdot x)/x = (2\cdot x + 1)/x
|
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