id
int64 -30,985
55.9k
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stringlengths 5
437k
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-20,518 |
\frac{s}{90 \cdot s} \cdot 20 = \frac{10 \cdot s}{s \cdot 10} \cdot 2/9
|
8,106 |
1/2 = \tfrac13 + \dfrac{1}{6}
|
2,314 |
\cos{x} = (e^{ix} + e^{-ix})/2 = \frac{1}{2e^{ix}}(e^{2ix} + 1)
|
15,394 |
\frac{7^{55}}{5^{72}} = (\frac{7^3}{5^4})^{18}\cdot 7
|
27,556 |
6\cdot 11 = 66 = \dfrac{11}{2}\cdot (11 + 1)
|
7,747 |
|-x_m + x_{m + 1}| = |x_m - x_{m + 1}|
|
19,234 |
((-1) + B)\cdot \left(1 + B^4 + B^3 + B^2 + B\right) = B^5 + (-1)
|
-22,637 |
-4/7\cdot \frac{5}{7} = \dfrac{1}{7\cdot 7}\cdot ((-4)\cdot 5) = -20/49 = -20/49
|
19,221 |
\cos{x} = \sin\left(x + π/2\right)
|
12,348 |
0.5\cdot y + x = 1.75 \Rightarrow 1.75 - 0.5\cdot y = x
|
-22,371 |
(p + 7 \cdot (-1)) \cdot \left(6 + p\right) = p^2 - p + 42 \cdot (-1)
|
6,175 |
0 = x^4 - 2 \cdot x^3 - 2 \cdot x + 1 = (x^2 - (1 + 3^{1/2}) \cdot x + 1) \cdot (x^2 - \left(1 - 3^{1/2}\right) \cdot x + 1)
|
8,138 |
\left(5 + y*5 = 20 \Rightarrow 15 = 5*y\right) \Rightarrow 3 = y
|
5,821 |
-\dfrac{55}{25}\cdot 25 + 80 + 25\cdot \left(-1\right) = 0
|
13,536 |
3 \cdot x \cdot x + x + 24 = -\frac{-287}{12} + 3 \cdot x \cdot x + x + 1/12
|
-8,104 |
21 = \frac{42}{2} \times 1
|
-4,427 |
\frac{8*(-1) - 5*x}{x^2 + 3*x + 2} = -\tfrac{2}{x + 2} - \frac{3}{x + 1}
|
-23,678 |
\frac{12}{35} = \dfrac{1}{7} \cdot 6 \cdot 2/5
|
25,521 |
(9 + x) (9(-1) + x) = 81 (-1) + x^2
|
10,208 |
\binom{g}{h} = \binom{g}{g - h}
|
-26,673 |
8x^2-18x-5=(4x+1)(2x-5)
|
-30,339 |
5 \cdot (-1) + 9 = 4
|
6,190 |
\frac16\cdot (1 + n)\cdot (1 + n + 1)\cdot (1 + (n + 1)\cdot 2) = 1^2 + 2^2 + 3 \cdot 3 + \ldots + n^2 + (n + 1) \cdot (n + 1)
|
28,679 |
\frac{5!}{2!}*2*5 = 600
|
-9,880 |
\phantom{ \dfrac{1}{1} \times -\dfrac{1}{1} \times -\dfrac{3}{5}} = \dfrac{1 \times -1 \times -3}{1 \times 1 \times 5} = \dfrac{3}{5}
|
14,203 |
x = x^1 = x^{0 + 1} = x^0 x^1 = xx = x \cdot x
|
14,750 |
-y^2 + x^2 = \left(-y + x\right)\cdot (x + y)
|
6,353 |
(m + k) h = -(-m - k) h = -(-m h + -k h) = --m h - -k h = mh + kh
|
-23,127 |
-\dfrac23 = -\dfrac{2}{3}
|
23,895 |
9025 - 190 \cdot s + s^2 = (95 - s) \cdot (95 - s)
|
11,222 |
\tfrac{1}{z + 1} = \dfrac{1}{(-1)*\left(-1\right) + z}
|
14,553 |
0 = 2 \cdot Z \cdot B_2^4 + 2 \cdot B_1 \cdot B_2^4 - 26 \cdot (Z \cdot B_2^2 + B_1 \cdot B_2^2) + 145 \geq \left(Z \cdot B_2^2 + B_1 \cdot B_2^2\right) \cdot \left(Z \cdot B_2^2 + B_1 \cdot B_2^2\right) - 38 \cdot (Z \cdot B_2^2 + B_1 \cdot B_2^2) + 1 + 18^2
|
11,910 |
\cos(\frac{\pi}{2} - w) = \sin{w}
|
25,411 |
6*(\frac{5}{4}) * (\frac{5}{4}) = 75/8 \lt 10
|
-28,766 |
\frac{1}{y + 2}\cdot \left((-1) + y^3\right) = y \cdot y - 2\cdot y + 4 - \frac{9}{y + 2}
|
-4,761 |
\dfrac{1}{z + 1}*4 - \frac{5}{3*(-1) + z} = \dfrac{17*(-1) - z}{3*(-1) + z^2 - z*2}
|
-5,467 |
\dfrac{1}{(7\cdot \left(-1\right) + k)\cdot 2} = \frac{1}{14\cdot (-1) + k\cdot 2}
|
-22,181 |
\tfrac{10}{2} = 5
|
-17,200 |
\dfrac{1}{\cos^2(\theta)} \times \cos^2(\theta) = \frac{1}{\cos^2(\theta)} \times (-\sin^2(\theta) + 1)
|
7,524 |
\pi*3/8 + \pi = \dfrac{11*\pi}{8}*1
|
27,254 |
7 - \left(2 + 1\right)*2/2 = 4
|
20,481 |
(a \cdot c)^n = a^n \cdot c^n = 1 \implies c^{-n} = a^n
|
-18,398 |
\frac{1}{9x + x^2}(63 + x^2 + x\cdot 16) = \frac{(9 + x) (7 + x)}{x\cdot (x + 9)}
|
-21,585 |
\cos(-\frac{4}{3}\pi) = -0.5
|
35,779 |
2 \cdot (k + 1) = 2 + k \cdot 2
|
18,663 |
\binom{n}{2} + \binom{n}{0} + \binom{n}{1} = \frac12\cdot (n^2 + n + 2)
|
24,830 |
z \cdot 7 - z \cdot 4 = 3 \cdot z
|
-20,362 |
\frac{7}{14 - 63 r} = \frac{7 \cdot \frac{1}{7}}{-9r + 2}
|
-480 |
\pi = 15 \cdot \pi - \pi \cdot 14
|
14,409 |
h\cdot x^n = x^n\cdot h
|
15,120 |
\sqrt{2}*\sqrt{2*\pi} = 2*\sqrt{\pi}
|
10,672 |
-2\cdot \sin^2{\frac{t}{2}} + 1 = \cos{t}
|
-578 |
e^{\pi\cdot i/3\cdot 14} = (e^{\pi\cdot i/3})^{14}
|
15,365 |
6 \cdot (-1) + n \cdot 3 = n + 4 \cdot (-1) + n + (-1) + n + \left(-1\right)
|
19,459 |
2^{2\cdot n + 2\cdot (-1)} = \left(2^{n + (-1)}\right)^2
|
11,741 |
-t + x_0 + i \cdot 2 = x_0 + i - t - i
|
28,177 |
|z + \left(-1\right)| = |z + \left(-1\right) + 0 \cdot (-1)| \leq |z + (-1)| + 0
|
2,818 |
-\tfrac{\cos^{1 + j}(y)}{j + 1} = \sin(y)\times \cos^j\left(y\right)
|
-19,098 |
\frac{1}{45}*2 = A_s/(36*\pi)*36*\pi = A_s
|
6,950 |
(10\cdot c + b) \cdot (10\cdot c + b) = 100\cdot c \cdot c + 20\cdot c\cdot b + b^2 = 10\cdot (10\cdot c^2 + 2\cdot c\cdot b) + b \cdot b
|
-19,511 |
\dfrac{\tfrac17 \cdot 9}{3 \cdot \dfrac{1}{8}} = 8/3 \cdot \frac97
|
-7,542 |
(-28 + 4*i + 21*i + 3)/25 = \left(-25 + 25*i\right)/25 = -1 + i
|
-2,547 |
\sqrt{4} \sqrt{6} + \sqrt{16} \sqrt{6} = 4\sqrt{6} + 2\sqrt{6}
|
-19,558 |
\frac72 \dfrac{1}{5} = \frac{7}{2 \cdot 5} = \dfrac{7}{10}
|
21,015 |
-h*x + n*x = x*(n - h)
|
-5,273 |
10^{9 + 5 \cdot (-1)} \cdot 5.3 = 10^4 \cdot 5.3
|
28,972 |
X\cdot X^n = X^{1 + n}
|
29,587 |
1 + 3(-1) = 6(-1) + 4
|
3,579 |
0 = 24 + 4\cdot y \Rightarrow -6 = y
|
1,780 |
2\cdot b\cdot x + 2\cdot y = 4 \implies y = 2 - x\cdot b
|
4,858 |
\dfrac{x + 1}{(-1) + x} = \frac{1}{\left(-1\right) + x}2 + 1
|
-26,554 |
-(3x)^2 + 10^2 = (-3x + 10) (x*3 + 10)
|
-8,370 |
-3 \times -2 = 6
|
13,578 |
\mathbb{E}((-\mathbb{E}(X) + X)^2) = -\mathbb{E}(X) \cdot \mathbb{E}(X) + \mathbb{E}(X^2)
|
-645 |
\frac{209}{12} \pi - 16 \pi = \frac{17}{12} \pi
|
-20,812 |
\frac{70}{56*(-1) - 14*t} = \dfrac17*7*\dfrac{10}{8*(-1) - t*2}
|
13,910 |
\frac{16}{3} = \tfrac{1}{4}*16 + 16/12
|
-2,063 |
-\pi/4 = -\pi \cdot \frac23 + \frac{5}{12} \cdot \pi
|
37,263 |
2+7+9=18
|
11,832 |
\left(x * x - 4*x + 13\right)*\left(x + 2\right)*(1 + x) = 26 + x^4 - x^3 + 3*x * x + 31*x
|
18,323 |
r \cdot (J + w) = J \cdot r + r \cdot w
|
13,182 |
( x^2, x\cdot z) = ( x \cdot x, x) \cap ( x^2, z) = x \cap ( x^2, z)
|
47,481 |
6 + 25 + 28 + 21 + 10 + 1 = 91
|
36,739 |
4^{2n} = 16^n
|
2,661 |
-(180 - B - Y) + 180 = B + Y
|
-6,384 |
\frac{1}{\left(8(-1) + q\right)*3} = \frac{1}{3q + 24 (-1)}
|
-3,269 |
\sqrt{6} \cdot \sqrt{9} + \sqrt{6} \cdot \sqrt{16} = \sqrt{6} \cdot 4 + \sqrt{6} \cdot 3
|
13,659 |
1 + y^2 = 10001 - (100 - y) (y + 100)
|
27,055 |
2036 = (503 + 499 \cdot (-1)) \cdot 509
|
4,063 |
\lambda^{-b} = \frac{1}{\lambda^b}
|
18,484 |
2 \times 6 =12
|
-20,310 |
\tfrac{1}{2*(-1) + t}*(2*(-1) + t)*(-5/6) = \dfrac{1}{6*t + 12*(-1)}*(-t*5 + 10)
|
49,817 |
910 = 182 \cdot 5
|
9,339 |
-\alpha \gt \beta \Rightarrow \alpha < -\beta
|
-30,112 |
\frac{\mathrm{d}}{\mathrm{d}z} z^k = k\cdot z^{k + \left(-1\right)}
|
14,198 |
\tan{x} = E/10\Longrightarrow 10*\tan{x} = E
|
29,442 |
-(-q - x) = x - q + q \cdot 2
|
20,303 |
\mathbb{E}\left((Q - \mathbb{E}\left(Q\right)) \cdot (-\mathbb{E}\left(x\right) + x)\right) = -\mathbb{E}\left(x\right) \cdot \mathbb{E}\left(Q\right) + \mathbb{E}\left(x \cdot Q\right)
|
26,738 |
3 + 11 + 19 = 33
|
3,034 |
k^3 = 12\cdot k - 5\cdot k^2 = 12\cdot k - 5\cdot (12 - 5\cdot k) = 37 - 60\cdot k
|
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