id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-7,730 |
\frac{1}{17} \cdot (-44 - 96 \cdot i + 11 \cdot i + 24 \cdot (-1)) = \dfrac{1}{17} \cdot (-68 - 85 \cdot i) = -4 - 5 \cdot i
|
8,005 |
(x - g) \cdot (-g + f) = x \cdot f + g^2 - (f + x) \cdot g
|
-28,906 |
\frac{1}{3} \cdot 30 = 10
|
50,754 |
17 + 80 + 145 + 204 + 213 + 204 + 145 = 1008
|
6,888 |
\frac{\dfrac{1}{9}}{\frac13}2 = 2/3
|
-25,470 |
7 (-1) - \sin{c} = \frac{d}{dc} (-7 c + \cos{c})
|
16,047 |
(\sqrt{2} + x^2)*(2^{\frac{1}{4}} + x)*(-2^{1/4} + x) = 2*(-1) + x^4
|
1,443 |
c/d + 1 = \frac{1}{d}*(c + d)
|
20,518 |
\frac{1}{k^n} \cdot k = \frac{1}{k^{\left(-1\right) + n}}
|
32,988 |
1 + 3p*2 = 1 + 6p
|
18,650 |
-h_2^k + h_1^k = (h_1 - h_2) (h_1^{k + (-1)} + h_1^{k + 2(-1)} h_2 + \dots + h_1 h_2^{2\left(-1\right) + k} + h_2^{k + \left(-1\right)})
|
18,620 |
26*(26*(26*(25 + (26*(26*25 + 25) + 25)*26) + 25) + 25) + 25 = 8031810175
|
19,540 |
(3\cdot y \cdot y)^2 = 3\cdot y \cdot y\cdot 3\cdot y^2 = 9\cdot y^4
|
28,684 |
y = \sin\left(2 \cdot q\right)\Longrightarrow 2 \cdot \cos(2 \cdot q) = \frac{\mathrm{d}y}{\mathrm{d}q}
|
23,228 |
W = \sin(\pi\cdot X\cdot 2) \implies X = \sin^{-1}\left(W\right)/(2\cdot \pi)
|
32,860 |
A \cdot A = 0 = 0\cdot A
|
12,881 |
\sin(\pi\times n + z) = \sin{\pi\times n}\times \cos{z} + \cos{\pi\times n}\times \sin{z} = (-1)^n\times \sin{z}
|
20,102 |
g_i g_j = g_i g_j
|
16,330 |
1 - z^n + z^n - z^{n + 1} = -z^{n + 1} + 1
|
2,583 |
z_2 = z_1 = 1/\left(z_2\right) + \dfrac{1}{z_1}
|
21,383 |
(\frac{37}{21})^3 + \left(\frac{17}{21}\right) \cdot \left(\frac{17}{21}\right) \cdot \left(\frac{17}{21}\right) = 6
|
3,093 |
\dfrac{1}{(k + 3)\cdot (k + 2)} = \frac{1}{k + 2} - \frac{1}{k + 3}
|
1,846 |
\dfrac{a}{x\cdot b} = \frac{1/b\cdot a}{x}
|
30,283 |
e^{x + z} = e^x*e^z
|
-25,493 |
\frac{\mathrm{d}}{\mathrm{d}r} (4\cdot r^3 + r) = 3\cdot 4\cdot r^2 + 1 = 12\cdot r \cdot r + 1
|
42,415 |
9 + 4 \cdot (-1) + 3 = 9 - 4 + 3 = 9 - 1 = 8
|
25,362 |
( h, I, x) = \left( I, x, h\right) = ( x, h, I)
|
25,930 |
y_2^2 + y_1^2 + \left(2 - y_1\right) \cdot \left(2 - y_1\right) = 4 \Rightarrow (y_1 + \left(-1\right))^2 + y_2^2/2 = 1
|
4,067 |
3 - 2x = x^2 + y^2 \Rightarrow (x + 1)^2 + y * y = 4
|
23,456 |
\cos\left(π/2 - z\right) = \sin{z}
|
-29,347 |
d^2 - \zeta^2 = (d - \zeta) (\zeta + d)
|
18,023 |
\int_0^x 1\,\mathrm{d}x = \int\limits_{q_0}^q 1\,\mathrm{d}q \implies q_0 + x = q
|
18,478 |
(1 - i)^{\frac14} = x + z*i \Rightarrow \left(z*i + x\right)^4 = -i + 1
|
26,715 |
(x \cdot x - x + 1)\cdot (x + 1) = 1 + x^3
|
-12,500 |
\dfrac{15}{7.5} = 2
|
-22,994 |
\frac{1}{110}*99 = 9*11/(10*11)
|
26,254 |
(c + (-1)) (7(-1) + c) = c^2 - c*8 + 7
|
-12,372 |
60 = 2^2*15
|
37,943 |
1400 = 2000 + 600*\left(-1\right)
|
21,731 |
d\cdot b = 1 \Rightarrow d\cdot b = 1
|
20,998 |
(b + c)*(-c + b) = -c^2 + b * b
|
10,520 |
3*\sin^2{a} + 5*(-1) = 3*\left(1 - \cos{2*a}\right)/2 + 5*\left(-1\right) = -(3*\cos{2*a} + 7)/2
|
-3,607 |
\frac{11}{8} y = y\cdot 11/8
|
30,621 |
R a = R \implies R a = R
|
4,154 |
\csc(\sin^{-1}{a/R}) = \frac{R}{a}
|
456 |
2 \cdot x^2 + D^2 + 3 \cdot D \cdot x = \left(2 \cdot x + D\right) \cdot (D + x)
|
13,448 |
\frac{1}{1 - 1 - y_i} = \frac{1}{y_i}
|
-1,650 |
\pi \dfrac{4}{3} + \frac{1}{12}11 \pi = 9/4 \pi
|
37,294 |
36 = \frac{3\cdot 4!}{2!}\cdot 1
|
41,117 |
1 = \tfrac{1}{\pi}*\pi
|
-7,160 |
\tfrac{5}{7}\cdot 3/7 = \frac{15}{49}
|
21,680 |
1 = 6079 \cdot 37469 - 15190 \cdot (52464 + 37469 \left(-1\right))
|
16,144 |
0 = (\frac{π}{2} - π/2)/2
|
23,008 |
x + x^2 + x^3 = \frac{x}{x + (-1)}((-1) + x^3)
|
7,132 |
13/2 \cdot ((13 + (-1)) + 2 \cdot h) = 13 \cdot (h + 6)
|
-10,515 |
4/4 (-6/(15 n)) = -\frac{24}{60 n}
|
-7,236 |
5/12*\frac{3}{13} = \tfrac{5}{52}
|
17,377 |
0 = 32\cdot A + 12\cdot E + 4 = 4\cdot A + 3\cdot E + 2
|
-22,932 |
130/117 = 13*10/\left(13*9\right)
|
26,361 |
-\frac13 \cdot 10 = -\frac43 + 2 \cdot \left(-1\right)
|
-16,378 |
3 \times \sqrt{175} = 3 \times \sqrt{25 \times 7}
|
-7,822 |
\tfrac{1}{13}(-9 + 45 i - 6i + 30 (-1)) = \frac{1}{13}(-39 + 39 i) = -3 + 3i
|
7,491 |
z^0 = \frac{1/z}{z^4}\cdot z^3\cdot z^2
|
36,207 |
\tan^4{x}*3 = 3*x + \frac{d}{dx} \tan^3{x} - \tan{x}*3
|
465 |
y^{m + k} = y^m\cdot y^k
|
3,569 |
(5 \cdot 5^{1/2})^3 = \left(5^{\dfrac12 \cdot 3}\right)^3 = 5^{9/2} = 5^4 \cdot \sqrt{5}
|
17,602 |
R - \frac12\cdot R = \dfrac{R}{2}
|
22,918 |
x = (3*(-1) + 20*x + 3)/20
|
1,365 |
\int (e \cdot f)^z\,dz = \int f^z \cdot e^z\,dz
|
-27,500 |
f^3\cdot 14 = 7\cdot f\cdot f\cdot f\cdot 2
|
-20,682 |
\dfrac{1}{4 - 2\cdot q}\cdot (4 - 2\cdot q)/8 = \frac{-q\cdot 2 + 4}{-q\cdot 16 + 32}
|
-26,511 |
36 x^2 = \left(6x\right)^2
|
11,505 |
x^9 + (-1) = x^{3^2} - 1^{3^2} = (x + \left(-1\right))^{3^2} = (x + (-1))^9
|
15,580 |
100 = 4 * 25
|
20,842 |
x^4 + 4 = x^4 + 4 \times x^2 + 4 - 4 \times x \times x = (x \times x + 2)^2 - (2 \times x)^2 = (x^2 + 2 \times x + 2) \times \left(x^2 - 2 \times x + 2\right)
|
10,855 |
x^{i + 2} \cdot \omega^{i + 2} = (x \cdot \omega)^{i + 2} = (x \cdot \omega)^{i + 1} \cdot x \cdot \omega = x^{i + 1} \cdot \omega^{i + 1} \cdot x \cdot \omega
|
-29,574 |
\frac1z\cdot (z^4 + z \cdot z\cdot 2 + 5\cdot \left(-1\right)) = \frac{1}{z}\cdot z^4 + \frac1z\cdot z \cdot z\cdot 2 - 5/z
|
5,920 |
\cos\left(x + \beta\right) = \cos{\beta} \cdot \cos{x} - \sin{x} \cdot \sin{\beta}
|
34,515 |
4 = 1!\cdot 2!\cdot 2!
|
-20,942 |
-\frac{12}{6 \cdot r + 54 \cdot (-1)} = -\frac{2}{r + 9 \cdot (-1)} \cdot 6/6
|
16,755 |
q \cdot r = (-(r \cdot r + q \cdot q) + (r + q)^2)/2
|
11,139 |
\left(100\% - 8\%\right)*(100\% - 38\%) = 57\%
|
19,808 |
\sin{\frac{\pi}{4}} = \cos{\tfrac{\pi}{4}} = \dfrac{1}{2} \cdot 2^{1/2}
|
5,751 |
\frac{1}{(-1) + t} - \dfrac{2}{t * t + (-1)} = \dfrac{1}{t + 1}
|
-12,800 |
\frac{5}{8} = \frac{1}{16}*10
|
4,613 |
0 = 16 + 9 \left(-1\right) + 7 (-1)
|
737 |
a = eae=e^{-1}ae
|
-4,901 |
\dfrac{1}{10}*3.8 = 3.8/10
|
24,828 |
\frac{q_1 q_2}{q_2 + q_1} = \tfrac{1}{\dfrac{1}{q_1} + \tfrac{1}{q_2}}
|
8,466 |
(6^2)^2 + (3 \times 3^2)^2 = 45 \times 45
|
27,204 |
\cos(c - b) = \cos(c) \cos(b) + \sin(c) \sin(b)
|
-10,542 |
1 = 4 \cdot p + 4 + 20 \cdot (-1) = 4 \cdot p + 167 \cdot (-1) = 4 \cdot p
|
-7,950 |
(-20 - 16\cdot i)/4 = -\tfrac{20}{4} - 16\cdot i/4
|
-19,047 |
1/5 = B_t/\left(100 \pi\right) \cdot 100 \pi = B_t
|
5,220 |
( x*2 + 10, 15 + 3 x, 17) = ( \left(x + 5\right)*2, (x + 5)*3, 17)
|
-4,487 |
(z + 4) \cdot (z + 2 \cdot (-1)) = z^2 + 2 \cdot z + 8 \cdot (-1)
|
16,840 |
\left(p p p - p^2\right)/2 = p^2\cdot (p + \left(-1\right))/2
|
2,319 |
(j + 1)*j! = \left(1 + j\right)!
|
23,090 |
-32 = 32*e^{i*\theta} = 32*(\cos{\theta} + i*\sin{\theta})
|
-2,316 |
-3/15 + \dfrac{1}{15}\cdot 8 = 5/15
|
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