Shalyt/ASyMOB-Algebraic_Symbolic_Mathematical_Operations_Benchmark

Index stringlengths 1 5	Challenge stringlengths 41 1.55k	Answer in Latex stringclasses 122 values	Answer in Sympy stringlengths 1 774	Variation stringclasses 31 values	Source stringclasses 61 values
101	Evaluate the iterated integral $\int_0^1dy\int_y^1 e^{-A (F x)^2}+B e^{F x} dx$. Assume A,B,F are real and positive.	\frac{2 A B \left(e^F (F-1)+1\right)-e^{-A F^2}+1}{2 A F^2}	(e*(AF*2)(2AB(eF(F - 1) + 1) + 1) - 1)/(2AF*2e*(AF**2))	Symbolic-3	MathOdyssey Problem 336 from Calculus and Analysis - College Math
102	What is the integral of $ 2 A x-B x^{7 F} \tan ^{-1}(3 G) $ Assume A,B,F,G are real and positive.	x \left(A x-\frac{B x^{7 F} \tan ^{-1}(3 G)}{7 F+1}\right)	x((Ax(7F + 1) - Bx(7F)atan(3G))/(7*F + 1))	Symbolic-4	GHOSTS Symbolic Integration Q97
103	What is the integral of $ (1 A) + B F x + \cosh (2 G) (F x)^{3 H} $ Assume A,B,F,G,H are real and positive.	A x+\frac{1}{2} B F x^2+\frac{x \cosh (2 G) (F x)^{3 H}}{3 H+1}	x(2(Fx)(3H)cosh(2G) + (2A + BFx)(3H + 1))/(2(3*H + 1))	Symbolic-5	GHOSTS Symbolic Integration Q98
104	What is the integral of $12 A+6 B \cosh (F x)$ Assume A,B,F are real and positive.	12 A x+\frac{6 B \sinh (F x)}{F}	12Ax + 6Bsinh(F*x)/F	Symbolic-3	GHOSTS Symbolic Integration Q90
105	What is the integral of $ 4 (B x)^{7 F}+G \sin ((1 H)+A x) $ Assume A,B,F,G,H are real and positive.	\frac{4 A x (B x)^{7 F}-(7 F+1) G \cos (H+A x)}{7 F A+A}	(4Ax(Bx)*(7F) - G(7F + 1)cos(H + Ax))/(A(7F + 1))	Symbolic-5	GHOSTS Symbolic Integration Q14
106	What is the integral of $ 2 x+2 B x^{2 F}+\frac{x}{G x+H x e^{A x}} $. Assume A,B,F,G,H are real and positive.	x \left(x+\frac{2 B x^{2 F}}{2 F+1}\right)-\frac{\log \left(G A \left(G+H e^{A x}\right)\right)}{G A}+\frac{\log \left(e^{A x}\right)}{G A}	(GAx((x(2F + 1) + 2Bx(2F))/(2F + 1)) + log(e(Ax)) - log(GA(G + He(Ax))))/(G*A)	Symbolic-5	GHOSTS Symbolic Integration Q7
107	What is the integral of $ B \log (3 H x) \cos (F \log (\sin (3)))-A x $ Assume A,B,F,H are real and positive.	B x (\log (3 H x)-1) \cos (F \log (\sin (3)))-\frac{A x^2}{2}	-Ax2/2 + Bx(log(3Hx) - 1)cos(F*log(sin(3)))	Symbolic-4	GHOSTS Symbolic Integration Q15
108	What is the integral of $ 3 A x - 4 B (H x)^2 \cos (F x+3 G) $ Assume A,B,F,G,H are real and positive.	\frac{3 A x^2}{2}-\frac{8 B H^2 x \cos (F x+3 G)}{F^2}-\frac{4 B H^2 \left(F^2 x^2-2\right) \sin (F x+3 G)}{F^3}	(3AF*3x*2 - 16BFH*2xcos(Fx + 3G) - 8BH2(F*2x*2 - 2)sin(Fx + 3G))/(2F*3)	Symbolic-5	GHOSTS Symbolic Integration Q18
109	What is the integral of $ A \tan ^{-1}(B x)+F \log (G \tanh (3 H))-3 $ Assume A,B,F,G,H are real and positive.	-\frac{A \log \left(B^2 x^2+1\right)}{2 B}+A x \tan ^{-1}(B x)+x (F \log (G \tanh (3 H))-3)	Axatan(Bx) - Alog(B*2x*2 + 1)/(2B) + x(Flog(Gtanh(3H)) - 3)	Symbolic-5	GHOSTS Symbolic Integration Q20
110	What is the integral of $ A (F x+4 G) (3 F x+4 G) e^{B x (F x+4 G)^2} $ Assume A,B,F,G are real and positive.	\frac{A e^{B x (F x+4 G)^2}}{B}	Ae(Bx(Fx + 4G)*2)/B	Symbolic-4	GHOSTS Symbolic Integration Q22
111	What is the integral of $ -A e^{3 B x} \sin \left(F e^{3 B x}\right) $ Assume A,B,F are real and positive.	\frac{A \cos \left(F e^{3 B x}\right)}{3 B F}	Acos(Fe*(3Bx))/(3B*F)	Symbolic-3	GHOSTS Symbolic Integration Q29
112	If $\log_{2 A} x - 2 F \log _{2 A} y=2 B$, determine $y$, as a function of $x$ Assume A,B,F are real and positive.	e^{\frac{2 F \log (2 A) \log (x)}{\log (2 A)-2 B \log(x)}}	e*(-2Flog(2A)log(x)/(2Blog(x) - log(2A)))	Symbolic-3	OlympiadBench oe_to_maths_en_comp 2498
113	If $f(x)=2 A x+ (1 B)$ and $g(f(x)) = 4 F x^{2}+ (1 G)$, determine an expression for $g(x)$.	\frac{F (x-B)^2}{A^2}+G	G + F(-B + x)2/A*2	Symbolic-4	OlympicArena Math_1381
114	Solve the following integral. Assume A,B,F are real and B>0. $\int_0^{\frac{\pi}{2 F}} \frac{A x \sin(2 F x)}{(1 B) + \cos^2(2 F x)} dx$	\frac{A\pi}{4F^2\sqrt{B}} \arctan\!\frac{1}{\sqrt{B}}	Apiatan(1/sqrt(B))/(4sqrt(B)F**2)	Symbolic-3	OBMU 2019 - Q21
115	Solve the following integral. Assume A,B,F,G are real and positive. $\int_{1}^{2} \frac{A e^{F x} (F x-1)}{F x \left(B e^{F x}+F G x\right)} dx$	-\frac{A \log \left(\frac{2 (e B+G)}{e^2 B+2 G}\right)}{B F}	-Alog((2(Be + G))/(Be*2 + 2G), E)/(B*F)	Symbolic-4	OBMU 2019 - Q18
116	Solve the following integral. Assume A,B,F are real and positive. Solve the following integral: $\int_{0}^{\pi} A \log(B (\sin(x))^{1 F}) dx$	A \pi \log\left(\frac{B}{2^F}\right)	A(pilog(B/(2**F), E))	Symbolic-3	OBMU 2019 - Q22
117	Evaluate the following hypergeometric function. Assume the parameters: A,B are real numbers. Return a closed-form symbolic answer. $ {}_2F_1\left( \begin{array}{c} 1 ,1 \\ 2 \end{array}; (-A)^B \right) $	-(-A)^{-B} \log \left(1-(-A)^B\right)	log(1 - (-A)B, E)/((-A)B)	Symbolic-2	ASyMOB Hypergeometrics Q1
118	Evaluate the following hypergeometric function. Assume the parameters: A,B are real numbers. Return a closed-form symbolic answer. $ {}_2F_1\left( \begin{array}{c} 1 ,1 \\ 3 \end{array}; -2 \cdot (A^B) \right) $	\frac{1}{2} A^{-2 B} \left(\left(2 A^B+1\right) \log \left(2 A^B+1\right)-2 A^B\right)	(-2(AB) + (2(A*B) + 1)log(2(AB) + 1, E))/(2(AB)2)	Symbolic-2	ASyMOB Hypergeometrics Q2
119	Evaluate the following hypergeometric function. Assume the parameters: A,B,G,H are real numbers. Return a closed-form symbolic answer. $ {}_8F_7\left( \begin{array}{c} 1,1,1, (1 A), (1 B), 1, (1 G), (1 H) \\ 2,2, (1 H), (1 G), (1 B), 1, (1 A) \end{array}; -1 \right) $	\frac{\pi ^2}{12}	pi**2/12	Symbolic-4	ASyMOB Hypergeometrics Q3
120	Evaluate the following hypergeometric function. Assume the parameters: x,A,B,G,H are real numbers. Return a closed-form symbolic answer. $ {}_3F_2\left( \begin{array}{c} -1,-A, -B \\ -H, -G \end{array}; x \right) $	1-\frac{A B x}{H G}	1 - A(Bx)/(H*G)	Symbolic-4	ASyMOB Hypergeometrics Q4
121	Solve the following integral. Assume the parameters: A,B,F are real numbers. Return a closed-form symbolic answer. $ \int \frac{ 1 A }{ 1 B + (x F)^3 } dx $	-\frac{A \left(\log \left(B^{2/3}-\sqrt[3]{B} F x+F^2 x^2\right)-2 \log \left(\sqrt[3]{B}+F x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 F x}{\sqrt[3]{B}}}{\sqrt{3}}\right)\right)}{6 B^{2/3} F}	-A(-2log(B*(1/3) + Fx) + log(B(2/3) - B(1/3)Fx + F*2x*2) + 2sqrt(3)atan(sqrt(3)(B*(1/3) - 2Fx)/(3B*(1/3))))/(6B*(2/3)F)	Symbolic-3	ASyMOB Hypergeometrics Q5
122	Solve the following integral. Assume A,B are positive integers. $ \int \frac{(4 A + (4 A - (1 B))x^{1 B})x^{2 A - 1}}{2 (1 + x^{1 B} + x^{4 A})\sqrt{1 + x^{1 B}}} dx $	\tan ^{-1}\left(\frac{\left x^A}{\sqrt{x^B+1}}\right)	atan(xA/(sqrt(xB + 1)))	Symbolic-2	ASyMOB Hypergeometrics Q6
123	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
124	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
125	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
126	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
127	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
128	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
129	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
130	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) e^{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
131	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
132	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) e^{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
133	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
134	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
135	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
136	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
137	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
138	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) e^{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
139	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
140	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) e^{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
141	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
142	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
143	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
144	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
145	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
146	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) e^{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
147	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
148	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) e^{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
149	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
150	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
151	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
152	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
153	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
154	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) e^{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
155	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
156	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) e^{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
157	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
158	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
159	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
160	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
161	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
162	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-All-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
163	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
164	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
165	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
166	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
167	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
168	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
169	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
170	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
171	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
172	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
173	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(9\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*59/15 - x*49/8 + x*29/2 + x*9 + 9	Numeric-One-1	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
174	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(13\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*513/15 - x*413/8 + x*213/2 + x*13 + 13	Numeric-One-2	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
175	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(974\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*5974/15 - x*4974/8 + x*2974/2 + x*974 + 974	Numeric-One-3	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
176	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(4561\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*54561/15 - x*44561/8 + x*24561/2 + x*4561 + 4561	Numeric-One-4	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
177	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(68222\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*568222/15 - x*468222/8 + x*268222/2 + x*68222 + 68222	Numeric-One-5	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
178	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(388580\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*5388580/15 - x*4388580/8 + x*2388580/2 + x*388580 + 388580	Numeric-One-6	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
179	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(2316065\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*52316065/15 - x*42316065/8 + x*22316065/2 + x*2316065 + 2316065	Numeric-One-7	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
180	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(97287075\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*597287075/15 - x*497287075/8 + x*297287075/2 + x*97287075 + 97287075	Numeric-One-8	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
181	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(326602299\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*5326602299/15 - x*4326602299/8 + x*2326602299/2 + x*326602299 + 326602299	Numeric-One-9	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
182	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(4615937897\right) e^{ \sin(x)} $, where A and B are symbolic constants.		-x*54615937897/15 - x*44615937897/8 + x*24615937897/2 + x*4615937897 + 4615937897	Numeric-One-10	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
183	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
184	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
185	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
186	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
187	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
188	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
189	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
190	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
191	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Easy	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
192	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \sin(x)} $, where A and B are symbolic constants.		-x5/15 - x4/8 + x**2/2 + x + 1	Equivalence-One-Hard	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
193	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(4\right) \sin(x)} $, where A and B are symbolic constants.		x*5(4 - 1043 + 45)/120 + x4(-442 + 44)/24 + x3(-4 + 43)/6 + x242/2 + x4 + 1	Numeric-One-1	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
194	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(49\right) \sin(x)} $, where A and B are symbolic constants.		x*5(49 - 10493 + 495)/120 + x4(-4492 + 494)/24 + x3(-49 + 493)/6 + x2492/2 + x49 + 1	Numeric-One-2	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
195	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(113\right) \sin(x)} $, where A and B are symbolic constants.		x*5(113 - 101133 + 1135)/120 + x4(-41132 + 1134)/24 + x3(-113 + 1133)/6 + x21132/2 + x113 + 1	Numeric-One-3	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
196	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(5969\right) \sin(x)} $, where A and B are symbolic constants.		x*5(5969 - 1059693 + 59695)/120 + x4(-459692 + 59694)/24 + x3(-5969 + 59693)/6 + x259692/2 + x5969 + 1	Numeric-One-4	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
197	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(92382\right) \sin(x)} $, where A and B are symbolic constants.		x*5(92382 - 10923823 + 923825)/120 + x4(-4923822 + 923824)/24 + x3(-92382 + 923823)/6 + x2923822/2 + x92382 + 1	Numeric-One-5	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
198	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(503855\right) \sin(x)} $, where A and B are symbolic constants.		x*5(503855 - 105038553 + 5038555)/120 + x4(-45038552 + 5038554)/24 + x3(-503855 + 5038553)/6 + x25038552/2 + x503855 + 1	Numeric-One-6	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
199	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(9004607\right) \sin(x)} $, where A and B are symbolic constants.		x*5(9004607 - 1090046073 + 90046075)/120 + x4(-490046072 + 90046074)/24 + x3(-9004607 + 90046073)/6 + x290046072/2 + x9004607 + 1	Numeric-One-7	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764
200	Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(55653951\right) \sin(x)} $, where A and B are symbolic constants.		x*5(55653951 - 10556539513 + 556539515)/120 + x4(-4556539512 + 556539514)/24 + x3(-55653951 + 556539513)/6 + x2556539512/2 + x55653951 + 1	Numeric-One-8	U-Math sequences_series 1ccc052c-9604-4459-a752-98ebdf3e0764

101

Evaluate the iterated integral $\int_0^1dy\int_y^1 e^{-A (F x)^2}+B e^{F x} dx$. Assume A,B,F are real and positive.

\frac{2 A B \left(e^F (F-1)+1\right)-e^{-A F^2}+1}{2 A F^2}

(e**(A*F**2)*(2*A*B*(e**F*(F - 1) + 1) + 1) - 1)/(2*A*F**2*e**(A*F**2))

Symbolic-3

MathOdyssey Problem 336 from Calculus and Analysis - College Math

102

What is the integral of $ 2 A x-B x^{7 F} \tan ^{-1}(3 G) $ Assume A,B,F,G are real and positive.

x \left(A x-\frac{B x^{7 F} \tan ^{-1}(3 G)}{7 F+1}\right)

x*((A*x*(7*F + 1) - B*x**(7*F)*atan(3*G))/(7*F + 1))

Symbolic-4

GHOSTS Symbolic Integration Q97

103

What is the integral of $ (1 A) + B F x + \cosh (2 G) (F x)^{3 H} $ Assume A,B,F,G,H are real and positive.

A x+\frac{1}{2} B F x^2+\frac{x \cosh (2 G) (F x)^{3 H}}{3 H+1}

x*(2*(F*x)**(3*H)*cosh(2*G) + (2*A + B*F*x)*(3*H + 1))/(2*(3*H + 1))

Symbolic-5

GHOSTS Symbolic Integration Q98

104

What is the integral of $12 A+6 B \cosh (F x)$ Assume A,B,F are real and positive.

12 A x+\frac{6 B \sinh (F x)}{F}

12*A*x + 6*B*sinh(F*x)/F

Symbolic-3

GHOSTS Symbolic Integration Q90

105

What is the integral of $ 4 (B x)^{7 F}+G \sin ((1 H)+A x) $ Assume A,B,F,G,H are real and positive.

\frac{4 A x (B x)^{7 F}-(7 F+1) G \cos (H+A x)}{7 F A+A}

(4*A*x*(B*x)**(7*F) - G*(7*F + 1)*cos(H + A*x))/(A*(7*F + 1))

Symbolic-5

GHOSTS Symbolic Integration Q14

106

What is the integral of $ 2 x+2 B x^{2 F}+\frac{x}{G x+H x e^{A x}} $. Assume A,B,F,G,H are real and positive.

x \left(x+\frac{2 B x^{2 F}}{2 F+1}\right)-\frac{\log \left(G A \left(G+H e^{A x}\right)\right)}{G A}+\frac{\log \left(e^{A x}\right)}{G A}

(G*A*x*((x*(2*F + 1) + 2*B*x**(2*F))/(2*F + 1)) + log(e**(A*x)) - log(G*A*(G + H*e**(A*x))))/(G*A)

Symbolic-5

GHOSTS Symbolic Integration Q7

107

What is the integral of $ B \log (3 H x) \cos (F \log (\sin (3)))-A x $ Assume A,B,F,H are real and positive.

B x (\log (3 H x)-1) \cos (F \log (\sin (3)))-\frac{A x^2}{2}

-A*x**2/2 + B*x*(log(3*H*x) - 1)*cos(F*log(sin(3)))

Symbolic-4

GHOSTS Symbolic Integration Q15

108

What is the integral of $ 3 A x - 4 B (H x)^2 \cos (F x+3 G) $ Assume A,B,F,G,H are real and positive.

\frac{3 A x^2}{2}-\frac{8 B H^2 x \cos (F x+3 G)}{F^2}-\frac{4 B H^2 \left(F^2 x^2-2\right) \sin (F x+3 G)}{F^3}

(3*A*F**3*x**2 - 16*B*F*H**2*x*cos(F*x + 3*G) - 8*B*H**2*(F**2*x**2 - 2)*sin(F*x + 3*G))/(2*F**3)

Symbolic-5

GHOSTS Symbolic Integration Q18

109

What is the integral of $ A \tan ^{-1}(B x)+F \log (G \tanh (3 H))-3 $ Assume A,B,F,G,H are real and positive.

-\frac{A \log \left(B^2 x^2+1\right)}{2 B}+A x \tan ^{-1}(B x)+x (F \log (G \tanh (3 H))-3)

A*x*atan(B*x) - A*log(B**2*x**2 + 1)/(2*B) + x*(F*log(G*tanh(3*H)) - 3)

Symbolic-5

GHOSTS Symbolic Integration Q20

110

What is the integral of $ A (F x+4 G) (3 F x+4 G) e^{B x (F x+4 G)^2} $ Assume A,B,F,G are real and positive.

\frac{A e^{B x (F x+4 G)^2}}{B}

A*e**(B*x*(F*x + 4*G)**2)/B

Symbolic-4

GHOSTS Symbolic Integration Q22

111

What is the integral of $ -A e^{3 B x} \sin \left(F e^{3 B x}\right) $ Assume A,B,F are real and positive.

\frac{A \cos \left(F e^{3 B x}\right)}{3 B F}

A*cos(F*e**(3*B*x))/(3*B*F)

Symbolic-3

GHOSTS Symbolic Integration Q29

112

If $\log_{2 A} x - 2 F \log _{2 A} y=2 B$, determine $y$, as a function of $x$ Assume A,B,F are real and positive.

e^{\frac{2 F \log (2 A) \log (x)}{\log (2 A)-2 B \log(x)}}

e**(-2*F*log(2*A)*log(x)/(2*B*log(x) - log(2*A)))

Symbolic-3

OlympiadBench oe_to_maths_en_comp 2498

113

If $f(x)=2 A x+ (1 B)$ and $g(f(x)) = 4 F x^{2}+ (1 G)$, determine an expression for $g(x)$.

\frac{F (x-B)^2}{A^2}+G

G + F*(-B + x)**2/A**2

Symbolic-4

OlympicArena Math_1381

114

Solve the following integral. Assume A,B,F are real and B>0. $\int_0^{\frac{\pi}{2 F}} \frac{A x \sin(2 F x)}{(1 B) + \cos^2(2 F x)} dx$

\frac{A\pi}{4F^2\sqrt{B}} \arctan\!\frac{1}{\sqrt{B}}

A*pi*atan(1/sqrt(B))/(4*sqrt(B)*F**2)

Symbolic-3

OBMU 2019 - Q21

115

Solve the following integral. Assume A,B,F,G are real and positive. $\int_{1}^{2} \frac{A e^{F x} (F x-1)}{F x \left(B e^{F x}+F G x\right)} dx$

-\frac{A \log \left(\frac{2 (e B+G)}{e^2 B+2 G}\right)}{B F}

-A*log((2*(B*e + G))/(B*e**2 + 2*G), E)/(B*F)

Symbolic-4

OBMU 2019 - Q18

116

Solve the following integral. Assume A,B,F are real and positive. Solve the following integral: $\int_{0}^{\pi} A \log(B (\sin(x))^{1 F}) dx$

A \pi \log\left(\frac{B}{2^F}\right)

A*(pi*log(B/(2**F), E))

Symbolic-3

OBMU 2019 - Q22

117

Evaluate the following hypergeometric function. Assume the parameters: A,B are real numbers. Return a closed-form symbolic answer. $ {}_2F_1\left( \begin{array}{c} 1 ,1 \\ 2 \end{array}; (-A)^B \right) $

-(-A)^{-B} \log \left(1-(-A)^B\right)

log(1 - (-A)**B, E)/((-A)**B)

Symbolic-2

ASyMOB Hypergeometrics Q1

118

Evaluate the following hypergeometric function. Assume the parameters: A,B are real numbers. Return a closed-form symbolic answer. $ {}_2F_1\left( \begin{array}{c} 1 ,1 \\ 3 \end{array}; -2 \cdot (A^B) \right) $

\frac{1}{2} A^{-2 B} \left(\left(2 A^B+1\right) \log \left(2 A^B+1\right)-2 A^B\right)

(-2*(A**B) + (2*(A**B) + 1)*log(2*(A**B) + 1, E))/(2*(A**B)**2)

Symbolic-2

ASyMOB Hypergeometrics Q2

119

Evaluate the following hypergeometric function. Assume the parameters: A,B,G,H are real numbers. Return a closed-form symbolic answer. $ {}_8F_7\left( \begin{array}{c} 1,1,1, (1 A), (1 B), 1, (1 G), (1 H) \\ 2,2, (1 H), (1 G), (1 B), 1, (1 A) \end{array}; -1 \right) $

\frac{\pi ^2}{12}

pi**2/12

Symbolic-4

ASyMOB Hypergeometrics Q3

120

Evaluate the following hypergeometric function. Assume the parameters: x,A,B,G,H are real numbers. Return a closed-form symbolic answer. $ {}_3F_2\left( \begin{array}{c} -1,-A, -B \\ -H, -G \end{array}; x \right) $

1-\frac{A B x}{H G}

1 - A*(B*x)/(H*G)

Symbolic-4

ASyMOB Hypergeometrics Q4

121

Solve the following integral. Assume the parameters: A,B,F are real numbers. Return a closed-form symbolic answer. $ \int \frac{ 1 A }{ 1 B + (x F)^3 } dx $

-\frac{A \left(\log \left(B^{2/3}-\sqrt[3]{B} F x+F^2 x^2\right)-2 \log \left(\sqrt[3]{B}+F x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 F x}{\sqrt[3]{B}}}{\sqrt{3}}\right)\right)}{6 B^{2/3} F}

-A*(-2*log(B**(1/3) + F*x) + log(B**(2/3) - B**(1/3)*F*x + F**2*x**2) + 2*sqrt(3)*atan(sqrt(3)*(B**(1/3) - 2*F*x)/(3*B**(1/3))))/(6*B**(2/3)*F)

Symbolic-3

ASyMOB Hypergeometrics Q5

122

Solve the following integral. Assume A,B are positive integers. $ \int \frac{(4 A + (4 A - (1 B))x^{1 B})x^{2 A - 1}}{2 (1 + x^{1 B} + x^{4 A})\sqrt{1 + x^{1 B}}} dx $

\tan ^{-1}\left(\frac{\left x^A}{\sqrt{x^B+1}}\right)

atan(x**A/(sqrt(x**B + 1)))

Symbolic-2

ASyMOB Hypergeometrics Q6

123

Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \sin(x)} $, where A and B are symbolic constants.

-x**5/15 - x**4/8 + x**2/2 + x + 1

Equivalence-All-Easy