id
int64
-30,985
55.9k
text
stringlengths
5
437k
-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