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ddrg
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math_formulas

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int64
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20,959
\left(d + 3\right)^2 = 3^2 + d \cdot 2 \cdot 3 + d^2
39,383
\sin(n\cdot \pi + \tfrac{\pi}{2}) = \sin\left(n\cdot \pi\right)\cdot \cos(\dfrac{\pi}{2}) + \cos(n\cdot \pi)\cdot \sin(\dfrac{\pi}{2}) = 0\cdot 0 + (-1)^n
3,141
5 + 6\cdot j = -((-1) - j)\cdot 6 - 1
38,115
9^2 - (-6)^2 = 45
404
1 + \sqrt{5} = (g + f \times \sqrt{5}) \times (c + x \times \sqrt{5}) = g \times c + 5 \times f \times x
5,347
\frac{n!}{m! (-m + n)!} = {n \choose m}
-24,977
\int_0^\pi ( 1, 2)*( -3*\sin(t), 3*\cos\left(t\right))\,dt = \int\limits_0^\pi (-3*\sin(t) + 6*\cos(t))\,dt = 3*\cos(t) + 6*\sin\left(t\right)
-17,786
53 (-1) + 59 = 6
-6,752
2/100 + \frac{1}{100}\cdot 70 = \frac{1}{100}\cdot 2 + \dfrac{1}{10}\cdot 7
-4,811
77.6\cdot 10^0 = 77.6\cdot 10^{2 - 2}
27,230
\tan{\alpha} = \frac{1}{\cos{\alpha}} \cdot \sin{\alpha}
5,335
((-3) \cdot \left(-1\right) + x) \cdot (x + 5 \cdot (-1)) = (3 + x) \cdot (5 \cdot \left(-1\right) + x)
12,929
\operatorname{acos}(\frac{1}{x^2 + 1} \cdot (x^2 + (-1))) = 2 \cdot y \implies \cos{y \cdot 2} = \frac{x^2 + (-1)}{1 + x \cdot x}
-25,789
4/40 = \frac{1}{8\cdot 5}\cdot 4
31,401
\frac{1}{233}*377 = 1 + 144/233
-16,763
6 = 20\cdot p^2 - 8\cdot p + 6\cdot (-5\cdot p) + 6\cdot 2 = 20\cdot p^2 - 8\cdot p - 30\cdot p + 12
35,130
\dfrac{1}{(2 + 2)^2} = 2^{2\cdot (-1) - 2}
-9,243
-y\cdot 2\cdot 2\cdot 3\cdot 5 + 2\cdot 3\cdot 3\cdot 5 = 90 - 60\cdot y
12,751
\frac{1}{y^2}\cdot x^2 = \frac{1}{1}\cdot 2 rightarrow 2 = x \cdot x, y^2 = 1
7,719
\frac{1}{x^{1 + m}}\times x = x^{-m}
15,718
\frac{5!}{2! \times 2!} = 120/4 = 30
17,511
\frac{1}{(2^l)^2} = \dfrac{1}{4^l}
-7,646
\frac{4 + i*19}{-5 - i*2} = \frac{19*i + 4}{-i*2 - 5}*\tfrac{1}{2*i - 5}*(-5 + i*2)
-5,634
\frac{1}{288 \cdot \left(-1\right) + q \cdot q \cdot 4 - q \cdot 4} \cdot (q \cdot 9 + 25 \cdot (-1)) = \frac{1}{288 \cdot (-1) + 4 \cdot q^2 - q \cdot 4} \cdot (4 \cdot q + 32 + 5 \cdot q + 45 \cdot (-1) + 12 \cdot (-1))
32,015
900 - 8*9*9 = 900 + 648*(-1) = 252
6,624
\xi^k = -1 \Rightarrow 1 = \xi^{k*2}
577
(W^2 + 3*(-1)) * (W^2 + 3*(-1)) + 8*(-1) = 1 + W^4 - W * W*6
-9,156
-49\cdot a^2 + 70\cdot a = -a\cdot a\cdot 7\cdot 7 + a\cdot 2\cdot 5\cdot 7
28,483
\cos^2\left(\frac{z}{2}\right)\times 4 + 2\times (-1) = 2\times \cos(z)
24,558
A \setminus E = A = A = A \cup (A \cap E)
-2,784
7 \cdot \sqrt{3} = \left(2 + 1 + 4\right) \cdot \sqrt{3}
30,808
z^3 - z^2 + 2 \cdot z + (-1) = z + 2 \cdot z^2 + 2 \cdot z + 2 = 2 \cdot z^2 + 2
49,626
\sin^2(x) \cos^3(x) = (\sin(x) \cos(x))^2 \cos(x) = (\sin(2x)/2)^2 \cos(x) = \tfrac{\sin^{22}(x) \cos(x)}{4}
-4,784
\frac{2}{x + 3} + \frac{3}{x + (-1)} = \frac{1}{x^2 + x\cdot 2 + 3\cdot (-1)}\cdot (x\cdot 5 + 7)
9,620
k^2*4 + k*8 + 4 = \left(k + 1\right)^2*4
23,388
\frac{1}{3*\frac23} = \frac{3*\frac{1}{2}}{3}
43,474
|z - 0| = |z| = |z-1|
-18,457
3\cdot c + 10\cdot (-1) = 9\cdot (c + 5\cdot \left(-1\right)) = 9\cdot c + 45\cdot (-1)
28,621
\tfrac{1}{a c} = \frac{1}{a c}
-7,381
\frac{1}{91}\cdot 10 = \frac{1}{13}\cdot 4\cdot \frac{5}{14}
21,209
\sin(2\cdot z) = 2\cdot \cos\left(z\right)\cdot \sin(z)
-7,075
\dfrac{1}{7}\cdot 2 = \frac{2}{7}
756
\cosh(x) = \frac12\cdot (e^x + e^{-x}) \leq e^{\dfrac{x^2}{2}}
-14,002
10*7 + 2*24/3 = 10*7 + 2*8 = 70 + 2*8 = 70 + 16 = 86
18,968
z*z = z^2 = z + 1
-6,986
\frac{6}{12} \cdot 4/11 = \frac{1}{11} \cdot 2
6,520
\frac{\binom{13}{4}}{39 \cdot \binom{13}{3} + \binom{13}{4}} = 5/83
6,210
\sin(\frac{1}{4}\pi + x) = \cos(x) \sin\left(\pi/4\right) + \sin(x) \cos\left(\frac{\pi}{4}\right)
-19,707
\frac{6\cdot 9}{7} = \dfrac17\cdot 54
-4,542
\frac{1}{Q + 5 \cdot (-1)} \cdot 4 - \frac{5}{Q + 3} = \tfrac{1}{Q \cdot Q - Q \cdot 2 + 15 \cdot (-1)} \cdot (-Q + 37)
-28,894
20! = 20*19*18 \ldots*3*2
14,321
(\cos(x) - \sin(x)) \cdot g \cdot x = dt \Rightarrow g \cdot x \cdot (\sin(x) - \cos(x)) = dt
-10,651
\frac44 \cdot \frac{9}{3 \cdot f^2} = \frac{1}{12 \cdot f^2} \cdot 36
-4,670
-\frac{1}{5 + z} + \frac{1}{5\times (-1) + z}\times 2 = \dfrac{1}{25\times (-1) + z^2}\times (15 + z)
-20,769
\frac{-30 \cdot y + 50}{y \cdot 36 + 60 \cdot (-1)} = -\frac56 \cdot \frac{10 \cdot (-1) + y \cdot 6}{10 \cdot (-1) + y \cdot 6}
10,612
(y + r)\cdot y = y\cdot y + r\cdot y = y\cdot y + r = y + r
-15,636
\frac{1}{q^{20}\cdot \frac{1}{p^3\cdot q}} = \dfrac{(\dfrac{1}{q^4})^5}{\dfrac{1}{p^3}\cdot 1/q}
19,433
(Z^Q\cdot x\cdot Y)^Q = Y^Q\cdot x^Q\cdot Z = Y^Q\cdot x\cdot Z
15,950
x^4 - z \cdot z x \cdot x\cdot 9 - 2x^2 z^2 + z^4 = z^4 + x^4 - x^2 z^2\cdot 11
-9,866
0.8 = \frac{1}{10}\cdot 8 = 4/5
11,391
\frac{1}{3}*(10002*\left(-1\right) + 99999) + 1 = 1 + \frac{1}{3}*(99999 + 10002*(-1))
28,390
(n + 1)\cdot (n + 2)\cdot n\cdot \ldots = \left(n + 2\right)!
-6,395
\dfrac{1}{(9 + n)\times 3} = \frac{1}{3\times n + 27}
4,700
2\cdot ((-3)\cdot (-1) + 10) = 26 - 3\cdot y\cdot z\cdot x \Rightarrow 26 + 26\cdot (-1) = 3\cdot x\cdot z\cdot y
27,017
\frac{x\cdot 1/h}{\frac{1}{g}\cdot f} = \frac{x}{h}\cdot g/f
9,151
\dfrac{1}{2} \times \left(4021 + 1\right) = 2011
26,789
9^2 * 9 - 3^3 - 2^3 = 694
3,783
341 = 10^0 + 10^2*3 + 4*10^1
6,369
\frac{\partial}{\partial z} (z^3 + y^3) = \frac{dy}{dz}\cdot y^2\cdot 3 + z^2\cdot 3
-7,794
\frac{1}{4 - i \cdot 4} \cdot (12 + i \cdot 12) = \dfrac{4 + i \cdot 4}{4 + i \cdot 4} \cdot \frac{1}{-i \cdot 4 + 4} \cdot (i \cdot 12 + 12)
35,690
\dfrac{1}{4} (8 + 512 + 8 + 32) = 140
25,743
Dg bD = bD gD
15,535
\mathbb{E}\left[X*U\right] = \mathbb{E}\left[U\right]*\mathbb{E}\left[X\right]
23,303
\int x^2 \cdot x\cdot x\,\mathrm{d}x + c = x^3\cdot y \Rightarrow x^5/5 + c = y\cdot x^3
7,298
1 = b \cdot a \implies 1 = a \cdot b
3,217
z^2\cdot z \cdot z = z^4
19,292
\tfrac{1}{1 + 1}\cdot (g + g) = 2\cdot g/2 = g/1 = g
-16,659
2 = 2(-3p) + 2 = -6p + 2 = -6p + 2
-10,485
\dfrac{4}{4}\cdot \frac{1}{t}\cdot (3\cdot t + 10\cdot (-1)) = \left(12\cdot t + 40\cdot (-1)\right)/(4\cdot t)
273
d^3 - c^2 \cdot c = (d - c) \cdot (d^2 + c \cdot d + c^2)
3,453
\left(0 = 2*x + 5*\left(-1\right) \Rightarrow 2*x = 5\right) \Rightarrow x = 5/2
-29,006
\dfrac12\cdot ((-1)\cdot 4.4 + 7.4) = 1.5
37,953
101 = 10 + 13*7
30,562
2/(\sqrt{3}) = \frac{\sqrt{3}}{3}2
1,205
\cos(y) \tan(y) = \sin\left(y\right)
-569
\left(e^{\tfrac{11}{12} \cdot \pi \cdot i}\right)^4 = e^{11 \cdot i \cdot \pi/12 \cdot 4}
17,558
(2\cdot x^2 + x\cdot 3 + 3)\cdot ((-1) + x) = (x + \left(-1\right))\cdot (1 + 2\cdot (x \cdot x + x + 1) + x)
-18,597
4 \cdot y + 2 \cdot (-1) = 6 \cdot (y + 9 \cdot (-1)) = 6 \cdot y + 54 \cdot (-1)
14,555
\frac{x}{x - y} \cdot y = \frac{1}{1/y - \dfrac1x}
24,806
\left(5 - 1.8\right) x + (9 - 3.7) x + (9 - 3.7) x = 3.2 x + 5.3 x + 5.3 x = 13.8 x
-2,002
\pi/3 + \frac{11}{12} \pi = \pi \frac{1}{4} 5
29,986
9/2 = (1 + 8)/2
8,493
c(ai+bj)=(ac)i+(bc)j
20,386
(g_1 \cdot g_2) \cdot (g_1 \cdot g_2) = g_1^2 \cdot g_2^2
37,259
-1 = \left\lfloor{z}\right\rfloor\Longrightarrow -1 \leq z < 0
-4,408
-\dfrac{1}{4 \cdot (-1) + z} + \frac{5}{2 \cdot (-1) + z} = \frac{18 \cdot \left(-1\right) + 4 \cdot z}{8 + z^2 - z \cdot 6}
15,746
n! = ((-1) + n)\cdot n\cdot \dots\cdot 2
24,343
x \cdot x + (-1) = (x + (-1)) \left(x + 1\right)
31,015
(-1) + 2 = (-7)*2 + 5*3
24,948
1 = -6\cdot z \implies -6 = z