$\mathrm{DONE}$

$\frac{N!}{\left(N+1\right)!}$

$\frac{1}{N+1}$

${\left(N+1\right)}^2{N!}^2$

${\left(N+1\right)!}^2$

$\sqrt{17}+4$

$1$

$\left[1,1,1,2\right]$

$1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}$

$4$

$\left[1,1,2,1,2,1,2,1,2\right]$

$\left(\begin{array}{cc}265& 97\\ 153& 56\end{array}\right)$

$1.7321428571428572$

$\left[1,1,1,2\right]$

$1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}$

$4$

$\left[1,1,2,1,2,1,2,1,2\right]$

$\left(\begin{array}{cc}265& 97\\ 153& 56\end{array}\right)$

$1.7321428571428572$

$\mathrm{DONE}$

$\mathrm{true}$

$F\left(BZ\right)+F\left(AY\right)+F\left(X\right)$

$\frac{1}{X+2}-\frac{1}{X+1}+\frac{1}{{\left(X+1\right)}^2}+X$

$Y+\frac{1}{X+1}+1$

$\left[A=0.5,B=3\right]$

$G\left(B\right)G\left(C\right)+G\left(A\right)$

$G\left(BC\right)+G\left(A\right)$

$\left[\left[A+3,4\right],\left[4,3.5\right]\right]$

$\left(A^2+2A+1\right)Y+X^2$

${\left(A+1\right)}^{2}Y+X^2$

$U{V}^{AX+B}+C$

$F\left(F\left(F\left(U\right)F\left({F\left(V\right)}^{F\left(F\left(F\left(A\right)F\left(X\right)\right)+F\left(B\right)\right)}\right)\right)+F\left(C\right)\right)$

$\left[Y+X,0,3.2,2.5\times {10}^{20},X\right]$

UNION(X,Y):=IF X = [] THEN Y
       ELSE (IF MEMBER(T:FIRST(X),Y) THEN UNION(REST(X),Y)
		 ELSE CONS(T,UNION(REST(X),Y)));

$\left[B,1,X^2,X^2,A,Y,\frac{1}{2}\right]$

$X^5-\frac{5X^4}{2}+\frac{5X^3}{3}-\frac{X}{6}$

$\left[1,\frac{5}{2},\frac{5}{3},\frac{1}{6}\right]$

$-\frac{5}{2}$

$\mathrm{DONE}$

$\frac{1}{3\left(\frac{{\left(2X-2^{\frac{1}{3}}\right)}^2}{32^{\frac{2}{3}}}+1\right)}-\frac{2X-2^{\frac{1}{3}}}{62^{\frac{2}{3}}\left(X^2-2^{\frac{1}{3}}X+2^{\frac{2}{3}}\right)}+\frac{1}{32^{\frac{2}{3}}\left(X+2^{\frac{1}{3}}\right)}$

$\frac{1}{X^3+2}$

$Negterm+Quotient+Quotient$

G(L):=CATCH(MAP(LAMBDA([X],IF X < 0 THEN THROW(X) ELSE F(X)),L));

$\left[F\left(1\right),F\left(2\right),F\left(3\right),F\left(7\right)\right]$

$-3$

$Y^2+BX$

$\mathrm{DONE}$

$BX+{\mathrm{\#101Y}}^2$

${\mathrm{\#101Y}}^2-Y^2$

$\left[Y\right]$

$BX+A^2$

$\mathrm{DONE}$

${\mathrm{\_101A}}^2+BX$

${\mathrm{\_101A}}^2-A^2$

$\left[A\right]$

$BX+A^2$

$\mathrm{DONE}$

${\mathrm{\_101A}}^2+BX$

${\mathrm{\_101A}}^2-A^2$

$\left[A\right]$

$\mathrm{DONE}$

$3F\left(B\right)+2F\left(A\right)$

$F\left(1,X\right)Y+2F\left(X,X\right)$

$\mathrm{DONE}$

$3F\left(B\right)+2F\left(A\right)$

$\mathrm{DONE}$

$2F\left(A\right)$

$\mathrm{DONE}$

$2F\left(A\right)F\left(B\right)$

$\mathrm{DONE}$

$G\left(G\left(G\left(A,B\right),C\right),D\right)$

$0$

$\mathrm{DONE}$

$G\left(G\left(G\left(A,B\right),C\right),D\right)$

$0$

$\mathrm{DONE}$

$H\left(X,Y,Z\right)$

$\mathrm{DONE}$

$H\left(X,Y,Z\right)$

$\mathrm{DONE}$

$-H\left(X,Y,Z\right)$

$\mathrm{DONE}$

$J\left(A,B,C,D\right)$

$\mathrm{DONE}$

$-F\left(X\right)$

$\mathrm{DONE}$

$G\left(X\right)$

$\mathrm{DONE}$

$\mathrm{true}$

$1$

$F$

$\left[\mathrm{HASHED},2,\left[1,X\right]\right]$

$\left[\mathrm{DECLARED},2,\left[2,3\right]\right]$

$\left[\mathrm{HASH\_TABLE},\mathrm{true},\left[1,x\right]\right]$

$\left[\right]$

$\left[{\mathrm{VAR}}_1>0\right]$

$\left[,{\mathrm{VAR}}_1>0\right]$

$2$

$\left[\mathrm{VALUE}\right]$

$R$

$R$

$\mathrm{DONE}$

$\left[R\right]$

$R$

$R$

$\mathrm{DONE}$

$\left[R\right]$

$\mathrm{TRANSCENDENTAL}$

$\mathrm{TRANSCENDENTAL}$

$\mathrm{false}$

TYPEOF(X):=BLOCK([Q],IF NUMBERP(X) THEN RETURN(ALGEBRAIC),
       IF NOT ATOM(X) THEN RETURN(MAPLIST(TYPEOF,X)),Q:GET(X,TYPE),
       IF Q = FALSE THEN ERROR("NOT NUMERIC") ELSE Q);

$\left[\mathrm{TRANSCENDENTAL},\left[\mathrm{false},\mathrm{TRANSCENDENTAL}\right]\right]$

$\mathrm{true}$

$\left[A>1\right]$

$\mathrm{true}$

$\mathrm{false}$

$\mathrm{true}$

$\mathrm{DONE}$

$\left[,\mathrm{SIMPEXPT}\right]$

$1-{\cos }^{2}Y$

$\mathrm{DONE}$

NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E));

$\mathrm{DONE}$

$\mathrm{LINEAR}$

$\left[B=Y^2,A=Y+4,X=Z\right]$

$\mathrm{DONE}$

CONSTINTERVAL(L,H):=CONSTANTP(H-L);

$\mathrm{DONE}$

$\mathrm{DONE}$

$\mathrm{DONE}$

$\left[B=X+2\pi ,A=X+\pi ,X=T,F=\sin T\right]$

$\mathrm{false}$

$\mathrm{DONE}$

$\mathrm{false}$

$\left[{\mathrm{SINRULE}}_1,\mathrm{SIMP-\%SIN}\right]$

$\sin X\cos \left(iY\right)+i\cos X\sinh Y$

$\mathrm{true}$

$\left[,\mathrm{SIMPEXPT}\right]$

$1$

$^$

$\left[,\mathrm{SIMPEXPT}\right]$

${\left(\sin X+1\right)}^2$

$2\sin X-{\cos }^{2}X+2$

$1-{\cos }^{2}X$

$\mathrm{DONE}$

$\mathrm{DONE}$

$\left[,\mathrm{SIMPEXPT}\right]$

$1-{\cos }^{2}Y$

$\mathrm{DONE}$

NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E));

$\mathrm{DONE}$

$\mathrm{LINEAR}$

$\left[B=Y^2,A=Y+4,X=Z\right]$

$\mathrm{DONE}$

CONSTINTERVAL(L,H):=CONSTANTP(H-L);

$\mathrm{DONE}$

$\mathrm{DONE}$

$\mathrm{DONE}$

$\left[B=X+2\pi ,A=X+\pi ,X=T,F=\sin T\right]$

$\mathrm{false}$

$\left[A,B,F,X\right]$

$\mathrm{DONE}$

ONELESS(X,Y):=IS(X = Y-1);

$\mathrm{MTEXT}\left(A_1{A}_2!,\mathrm{-->},A_1!,\mathrm{WHERE},\mathrm{ONELESS}\left(A_2,A_1\right)\right)$

$\mathrm{MTEXT}\left(\frac{A_1!}{A_1},\mathrm{-->},\left(A_1-1\right)!\right)$

$\left(M-1\right)!N!$

$\mathrm{MTEXT}\left({\sin }^{2}A,\mathrm{-->},1-{\cos }^{2}A\right)$

${\sin }^{4}X$

${\cos }^{4}X-2{\cos }^{2}X+1$

$\mathrm{DONE}$

ONELESS(X,Y):=IS(X = Y-1);

$\mathrm{MTEXT}\left(A_1{A}_2!,\mathrm{-->},A_1!,\mathrm{WHERE},\mathrm{ONELESS}\left(A_2,A_1\right)\right)$

$\mathrm{MTEXT}\left(\frac{A_1!}{A_1},\mathrm{-->},\left(A_1-1\right)!\right)$

$\left(M-1\right)!N!$

$\mathrm{MTEXT}\left({\sin }^{2}A,\mathrm{-->},1-{\cos }^{2}A\right)$

${\sin }^{4}X$

${\cos }^{4}X-2{\cos }^{2}X+1$

$\mathrm{true}$

$\frac{1}{2}-\frac{1}{2}\cos \left(2X\right)$

$\left(2A^2-B\right)\cos \left(2Y+X\right)+\left(AB+5\right)\sin \left(4X-U\right)$

$\frac{1}{2}{\left(2A^2-B\right)}^2\cos \left(4Y+2X\right)-\left(2A^2-B\right)\left(AB-5\right)\sin \left(2Y+5X-U\right)+\left(2A^2-B\right)\left(AB-5\right)\sin \left(2Y-3X+U\right)-\frac{1}{2}{\left(AB-5\right)}^2\cos \left(8X-2U\right)+\frac{1}{2}{\left(AB-5\right)}^2+\frac{1}{2}{\left(2A^2-B\right)}^2$

$\mathrm{DONE}$

$\frac{1}{8}{\left(2A^2-B\right)}^2\sin \left(4Y+2X\right)-\frac{1}{2}\left(B-2A^2\right)\left(AB-5\right)\cos \left(2Y+5X-U\right)-\frac{1}{2}\left(2A^2-B\right)\left(AB-5\right)\cos \left(2Y-3X+U\right)$

$\frac{1}{8}{\left(2A^2-B\right)}^2\sin \left(4Y+2X\right)-\frac{1}{2}\left(B-2A^2\right)\left(AB-5\right)\cos \left(2Y+5X-U\right)-\frac{1}{2}\left(2A^2-B\right)\left(AB-5\right)\cos \left(2Y-3X+U\right)$

$\frac{1}{16}\sin \left(5X\right)+\frac{1}{16}\cos \left(5X\right)-\frac{5}{16}\sin \left(3X\right)+\frac{5}{16}\cos \left(3X\right)+\frac{5}{8}\sin X+\frac{5}{8}\cos X$

$\mathrm{false}$

$X^2\left(\frac{d}{dX}Y\right)+3XY=\frac{\sin X}{X}$

$Y=\frac{\mathrm{\%C}-\cos X}{X^3}$

$Y=-\frac{\cos X+1}{X^3}$

$\frac{d^2}{d{X}^2}Y+Y{\left(\frac{d}{dX}Y\right)}^3=0$

$\frac{Y^3+6{\mathrm{\%K}}_{1}Y}{6}=X+{\mathrm{\%K}}_2$

$-\frac{2Y^3-3Y}{6}=X$

$\frac{Y^3-10Y}{6}=X-\frac{3}{2}$

$-K^2{L}^2{M}^2{N}^2+K^2{M}^2{N}^2-K^2{L}^2{N}^2+K^2{N}^2$

$L^2+K^2=1$

$N^2-M^2=1$

$K^4{N}^4$

$\frac{K_1{K}_4-K_2{K}_3-K_1{K}_2}{{K_3}^2}$

$K_1{K}_4-K_2{K}_3=0$

$K_3{K}_4+K_1{K}_2=0$

$\frac{K_4}{K_3}$

$Z+XY+2X^2$

$-Z+5Y+3X-1$

$Z^2-Y^2+X+5$

$\left[7425X^8-1170X^7+1299X^6+12076X^5+22887X^4-5154X^3-1291X^2+7688X+15376\right]$

$\frac{d}{dX}F\left(X\right)=\frac{d}{dX}G\left(X\right)+\sin X$

$\frac{d^2}{d{X}^2}G\left(X\right)=\frac{d}{dX}F\left(X\right)-\cos X$

$A$

$1$

$\{$

$|$

$\{\left(|\left(X,X\right)>0\right)$

$\{\left(|\left(X,X\right)<2\right)$

$\mathrm{OU}$

$\mathrm{OI}$

$\mathrm{OU}\left(\{\left(|\left(X,X\right)>0\right),\{\left(|\left(X,X\right)<2\right)\right)$

$\mathrm{OU}\left(\{\left(|\left(X,X\right)>0\right),\{\left(|\left(X,X\right)<2\right)\right)$

$\{\left(1,2,3\right)$

$\{\left(3,4,5\right)$

$\mathrm{OU}\left(\mathrm{OU}\left(\{\left(1,2,3\right),\{\left(1,2,3\right)\right),\{\left(3,4,5\right)\right)$

$\mathrm{OU}$

$\mathrm{OI}$

$\mathrm{OU}\left(\mathrm{OU}\left(\{\left(1,2,3\right),\{\left(1,2,3\right)\right),\{\left(7\right)\right)$

$\mathrm{DONE}$

$\mathrm{true}$

$\mathrm{true}$

$\frac{3\Gamma \left(\frac{3}{4}\right)b^{\frac{7}{8}}{e}^{\frac{b{p}^2}{4}}\left(\frac{8\sqrt{\pi }{\mathrm{\%M}}_{-\frac{5}{8},-\frac{1}{4}}(\frac{b{p}^2}{2})}{32^{\frac{5}{8}}\Gamma \left(\frac{3}{8}\right)b^{\frac{1}{4}}\sqrt{p}}-\frac{2^{\frac{3}{8}}\sqrt{\pi }{\mathrm{\%M}}_{-\frac{5}{8},\frac{1}{4}}(\frac{b{p}^2}{2})}{\Gamma \left(\frac{7}{8}\right)b^{\frac{1}{4}}\sqrt{p}}\right)}{4}$

$\frac{\sqrt{2}{e}^{\frac{A}{2p}}\left(\frac{\sqrt{\pi }{e}^{\frac{A}{2p}}}{\sqrt{2}}-\frac{\sqrt{2}\sqrt{\pi }\mathrm{erf}\left(\frac{\sqrt{A}}{\sqrt{p}}\right)e^{\frac{A}{2p}}}{2}\right)}{\sqrt{p}}$

$-\frac{\sqrt{\pi }{e}^{\left(\frac{p^2+2iAp+A^2}{4b}\right)}\left(e^{\frac{2iAp+A^2}{2b}}\mathrm{erf}\left(\frac{ip+A}{2\sqrt{b}}\right)-e^{\frac{A^2}{2b}}\mathrm{erf}\left(\frac{ip-A}{2\sqrt{b}}\right)+i{e}^{\frac{p^2+2iAp}{2b}}\mathrm{erf}\left(\frac{p+iA}{2\sqrt{b}}\right)-i{e}^{\frac{p^2}{2b}}\mathrm{erf}\left(\frac{p-iA}{2\sqrt{b}}\right)+\left(i-i{e}^{\frac{iAp}{b}}\right)e^{\frac{p^2}{2b}}-e^{\frac{2iAp+A^2}{2b}}+e^{\frac{A^2}{2b}}\right)}{8\sqrt{b}}$

$\frac{\sqrt{A}{e}^{\left(\frac{A}{p}\right)}}{p^2}$

$\frac{16\left(2p\sqrt{p^2+1}+2p^2\right)}{9{\pi }^{\frac{3}{2}}{p}^4\left(2p\sqrt{p^2+1}+2p^2+1\right)}$

$\frac{e^{\left(\frac{1}{4p}\right)}\left(\sqrt{p}\left(140p+10\right)e^{\frac{1}{4p}}+\sqrt{\pi }\left(140i\mathrm{erf}\left(\frac{i}{2\sqrt{p}}\right)p^2+20i\mathrm{erf}\left(\frac{i}{2\sqrt{p}}\right)p+5i\mathrm{erf}\left(\frac{i}{2\sqrt{p}}\right)\right)\right)}{8\pi p^4}$

$\frac{{\mathrm{\%IBES}}_0(\frac{At}{2}){\mathrm{\%IBES}}_1(\frac{At}{2})}{p^2}$

$\frac{2i\left(\frac{1}{{\left(\frac{2i}{p}+1\right)}^{\frac{3}{4}}}-\frac{1}{{\left(1-\frac{2i}{p}\right)}^{\frac{3}{4}}}\right)}{2^{\frac{3}{4}}\Gamma \left(\frac{1}{4}\right)p^{\frac{3}{2}}}$

$-\frac{12\left(\frac{-\frac{3\sqrt{\pi }i\mathrm{erf}\left(\frac{i}{\sqrt{p}}\right)p^{\frac{5}{2}}{e}^{\left(\frac{1}{p}\right)}}{8}-\frac{\sqrt{\pi }i\mathrm{erf}\left(\frac{i}{\sqrt{p}}\right)p^{\frac{3}{2}}{e}^{\left(\frac{1}{p}\right)}}{2}-\frac{\sqrt{\pi }i\mathrm{erf}\left(\frac{i}{\sqrt{p}}\right)\sqrt{p}{e}^{\left(\frac{1}{p}\right)}}{2}-\frac{3p^2}{4}-\frac{p}{2}}{p^2}+\frac{2\left(\frac{\sqrt{\pi }i\mathrm{erf}\left(\frac{i}{\sqrt{p}}\right)p^{\frac{3}{2}}{e}^{\left(\frac{1}{p}\right)}}{4}+\frac{\sqrt{\pi }i\mathrm{erf}\left(\frac{i}{\sqrt{p}}\right)\sqrt{p}{e}^{\left(\frac{1}{p}\right)}}{2}+\frac{p}{2}\right)}{p}-\frac{\sqrt{\pi }i\mathrm{erf}\left(\frac{i}{\sqrt{p}}\right)\sqrt{p}{e}^{\left(\frac{1}{p}\right)}}{2}\right)}{\pi p^4}$

$-\frac{i\mathrm{erf}\left(\frac{i}{\sqrt{p}}\right)e^{\left(\frac{1}{p}\right)}}{\sqrt{\pi }{p}^{\frac{3}{2}}}$

$\frac{\sqrt{\pi }{\mathrm{\%IBES}}_1(t)}{2p^{\frac{3}{2}}}$

$-\frac{4i\Gamma \left(\frac{1}{3}\right){\mathrm{\%M}}_{-\frac{3}{2},\frac{1}{3}}(-\frac{1}{4p})e^{\left(\frac{1}{8p}\right)}}{3{\left(1\right)}^{\frac{5}{6}}\sqrt{3}\Gamma \left(\frac{2}{3}\right)p^{\frac{3}{2}}}+\frac{4\Gamma \left(\frac{1}{3}\right){\mathrm{\%M}}_{-\frac{3}{2},\frac{1}{3}}(-\frac{1}{4p})e^{\left(\frac{1}{8p}\right)}}{3{\left(1\right)}^{\frac{5}{6}}\Gamma \left(\frac{2}{3}\right)p^{\frac{3}{2}}}-\frac{8i\Gamma \left(\frac{2}{3}\right){\mathrm{\%M}}_{-\frac{3}{2},-\frac{1}{3}}(-\frac{1}{4p})e^{\left(\frac{1}{8p}\right)}}{3{\left(1\right)}^{\frac{1}{6}}\sqrt{3}\Gamma \left(\frac{1}{3}\right)p^{\frac{3}{2}}}$

$\frac{5i\Gamma \left(\frac{1}{4}\right){\mathrm{\%P}}_{-\frac{3}{2},-\frac{3}{4}}(\frac{1}{\sqrt{\frac{1}{p^2}+1}}){\left(\frac{1}{p^4}-1\right)}^{\frac{3}{8}}{p}^{\frac{9}{4}}}{18{\left(1\right)}^{\frac{1}{4}}\sqrt{2}{\Gamma }^2\left(\frac{3}{4}\right)}+\frac{5\Gamma \left(\frac{1}{4}\right){\mathrm{\%P}}_{-\frac{3}{2},-\frac{3}{4}}(\frac{1}{\sqrt{\frac{1}{p^2}+1}}){\left(\frac{1}{p^4}-1\right)}^{\frac{3}{8}}{p}^{\frac{9}{4}}}{18{\left(1\right)}^{\frac{1}{4}}\sqrt{2}{\Gamma }^2\left(\frac{3}{4}\right)}+\frac{4i\Gamma \left(\frac{3}{4}\right){\mathrm{\%P}}_{-\frac{3}{2},\frac{3}{4}}(\frac{1}{\sqrt{\frac{1}{p^2}+1}})p^{\frac{3}{4}}}{{\left(1\right)}^{\frac{3}{4}}{\Gamma }^2\left(\frac{1}{4}\right){\left(\frac{1}{p^4}-1\right)}^{\frac{3}{8}}}$

$\frac{4}{\sqrt{2}\sqrt{\pi }{\left(\frac{1}{p^2}+1\right)}^2{p}^3}-\frac{\sqrt{2}i\left(\frac{1}{\frac{1}{p^2}+1}-\frac{1}{{\left(\frac{1}{p^2}+1\right)}^2{p}^2}\right)}{\sqrt{\pi }{p}^2}$

$\frac{15i{\left(\frac{1}{A^2+1}-1\right)}^{\frac{3}{4}}\left(\frac{1}{{\left(\sqrt{A^2+1}+1\right)}^{\frac{3}{2}}}+\frac{1}{{\left(1-\sqrt{A^2+1}\right)}^{\frac{3}{2}}}\right)}{16\sqrt{A^2+1}}$

$\frac{3A}{{\left(\frac{A^2}{p^2}+1\right)}^{\frac{5}{2}}{p}^4}$

$\frac{\sqrt{A}{e}^{\left(\frac{A}{p}\right)}}{p^2}$

$\mathrm{DONE}$

$\left[\mathrm{TR\_OPTIMIZE\_MAX\_LOOP}\right]$

$\frac{3^{\left(\frac{1}{\log 3}+1\right)\log x}}{\left(\frac{1}{\log 3}+1\right)\log 3}$

$-\frac{4}{3}$

$\left[1,2,3,4,5,6,7,8,9,10\right]$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$\mathrm{true}$

$\frac{d}{dy}f\left(x,y\right)$

$\frac{d}{dx}f\left(x,y\right)$

h(x,y):=x*y*DIFF(f(x,y),x,1,y,1);

F(X):=Y+X^2;

$Y+4$

$11$

F(X):=1+SIN(X)^2;

${\sin }^2\left(X+1\right)+1$

G(Y,Z):=3*Y+F(Z);

$3\left(Z+14\right)+1.2298488470659301$

H(N):=SUM(I*X^I,I,0,N);

$\left[F\left(X\right),G\left(Y,Z\right),H\left(N\right)\right]$

T[N](X):=RATEXPAND(2*X*T[N-1](X)-T[N-2](X));

T[0](X):=1;

T[1](X):=X;

$8Y^4-8Y^2+1$

G[N](X):=SUM(EV(X),I,N,2+N);

H(N,X):=SUM(EV(X),I,N,2+N);

$3I^2$

$29$

P[N](X):=RATSIMP(DIFF((X^2-1)^N,X,N)/(2^N*N!));

Q(N,X):=RATSIMP(DIFF((X^2-1)^N,X,N)/(2^N*N!));

$\mathrm{LAMBDA}\left(\left[X\right],\frac{3X^2-1}{2}\right)$

$\frac{3{\left(Y+1\right)}^2-1}{2}$

$\frac{3Y^2-1}{2}$

$37$

F[I,J](X,Y):=Y^J+X^I;

G(FUN,A,B):=PRINT(FUN," applied to ",A," and ",B," is ",FUN(A,B));

$2C$

$1.5403023064268146$

$\mathrm{DONE}$

A[N]:=N*A[N-1];

$1$

$120$

A[N]:=N;

$6$

$24$

$\mathrm{LAMBDA}\left(\left[X,Y,Z\right],Z^2+Y^2+X^2\right)$

$A^2+5$

$A+3$

$\left[X^2,\frac{Y}{3},2\right]$

$X^3$

$\left[A,\left[X^2,\frac{Y}{3},2\right],X^3\right]$

$\left(\begin{array}{cc}A& 0\\ B& 1\end{array}\right)$

$\left(\begin{array}{cc}{A}^2& 0\\ B^2& 1\end{array}\right)$

$\left(\begin{array}{cc}{A}^2& 0\\ AB+B& 1\end{array}\right)$

$\left(\begin{array}{cc}{A}^2& 0\\ AB& A\end{array}\right)$

$\left(\begin{array}{cc}1& 1\\ 1-B& A\end{array}\right)$

$\left(\begin{array}{cc}\frac{1}{A}& 0\\ -\frac{B}{A}& 1\end{array}\right)$

$\left(\begin{array}{cc}BY+AX& Y\end{array}\right)$

$\left(\begin{array}{ccc}A& B& C\\ D& E& F\\ G& H& I\end{array}\right)$

$\left(\begin{array}{ccc}CG+BD+A^2& CH+BE+AB& CI+BF+AC\\ FG+DE+AD& FH+E^2+BD& FI+EF+CD\\ GI+DH+AG& HI+EH+BG& I^2+FH+CG\end{array}\right)$

$X+1=Y^2$

$X-1=2Y+1$

$2X=Y^2+2Y+1$

$\frac{X+1}{Y}=Y$

$\frac{Y}{X+1}=\frac{1}{Y}$

FIB[N]:=IF N = 1 OR N = 2 THEN 1 ELSE FIB[N-2]+FIB[N-1];

$2$

$2$

$5$

ETA(MU,NU):=IF MU = NU THEN MU ELSE (IF MU > NU THEN MU-NU ELSE NU+MU);

$11$

$4$

$A$

$\mathrm{DONE}$

HESSIAN(F):=BLOCK([DFXX,DFXY,DFXZ,DFYY,DFYZ,DFZZ],DFXX:DIFF(F,X,2),
	DFXY:DIFF(F,X,1,Y,1),DFXZ:DIFF(F,X,1,Z,1),DFYY:DIFF(F,Y,2),
	DFYZ:DIFF(F,Y,1,Z,1),DFZZ:DIFF(F,Z,2),
	DETERMINANT(MATRIX([DFXX,DFXY,DFXZ],[DFXY,DFYY,DFYZ],
			   [DFXZ,DFYZ,DFZZ])));

$\mathrm{DONE}$

$-3AY\left(9A^{2}XZ+18A{Y}^2\right)-27A^{3}XYZ-54A^2{X}^3$

$Y^3+AXY+X^3$

F(X):=BLOCK([A,Y],LOCAL(A),Y:4,A[Y]:X,DISPLAY(A[Y]));

$2$

$0$

$\mathrm{DONE}$

$0$

$\mathrm{DONE}$

$0$

$\mathrm{DONE}$

$55$

$1$

$e^{\sin X}$

$\mathrm{DONE}$

$\frac{X^7}{90}-\frac{X^6}{240}-\frac{X^5}{15}-\frac{X^4}{8}+\frac{X^2}{2}+X+1$

$0$

$\mathrm{DONE}$

$5X^5+9X^4+12X^3+14X^2+15X$

$-3.0$

$\mathrm{DONE}$

$1000$

$\mathrm{DONE}$

$2.2824290358878674$

$\left[X\right]$

NEWTON(F,GUESS):=BLOCK([NUMER,Y],LOCAL(F,DF,X,GUESS),NUMER:TRUE,
       DEFINE(DF(X),DIFF(F(X),X)),
       DO (Y:DF(GUESS),IF Y = 0 THEN ERROR("derivative at",GUESS,"is zero"),
	   GUESS:GUESS-F(GUESS)/Y,
	   IF ABS(F(GUESS)) < 5.0E-6 THEN RETURN(GUESS)));

SQR(X):=X^2-5.0;

$\mathrm{DONE}$

$E_{90}$

$\mathrm{DONE}$

$\mathrm{DONE}$

$X\left(\frac{d}{dX}F\left(X\right)\right)+F\left(X\right)$

F(X):=SIN(X);

$\sin X+X\cos X$

$X$

$3$

$3$

$X$

F(X):=X^2;

$F\left(2\right)$

$4$

$F\left(2\right)$

$4$

$33$

$\sum _{I=1}^{4}I!$

$\left[X\right]$

$\mathrm{DONE}$

$S+55$

$55$

$S+110$

$\sum _{I=0}^{N}G\left(I\right)$

$Z{e}^Z$

$X^2{e}^{X^2}$

$\sum _{I=0}^{N}G\left(I\right)$

$\sum _{I=0}^{N}G\left(I\right)$

$\sum _{I=0}^{N}G\left(I\right)+1$

$\mathrm{DONE}$

$A$

$\mathrm{DONE}$

$\frac{Y^3}{3}$

F(Y):=DIFF(Y*LOG(Y),Y,2);

F(Y):=1/Y;

$\mathrm{tmp}:\%$

${\left(Y+X\right)}^3$

$3{\left(Y+X\right)}^2$

$X^2+1$

$\sin X$

$\sin \left(\frac{\pi }{12}\right)+\frac{1}{\sqrt{3}}$

$\sin 1$

$\beta \left(\frac{1}{2},\frac{2}{5}\right)$

$\frac{1}{2\left(1-X\right)\sqrt{X}}$

$25$

$4.79425538604203000\; 2732879B-1$

${\cos }^{2}X-{\sin }^{2}X$

$-\frac{1}{2}$

$-4\cos X\sin X$

$\frac{\frac{\sin \left(2X\right)}{2}+X}{2}-\frac{X-\frac{\sin \left(2X\right)}{2}}{2}$

$\frac{\sin \left(2X\right)}{2}$

$\cos X\sin X$

$\frac{\sin \left(2X\right)}{2}$

$\cos \left(2X\right)$

$\frac{{\mathrm{sech}}^{2}X\sinh X\tanh X}{{\coth }^{2}X}+\frac{{\cosh }^{2}X{\mathrm{sech}}^{2}X\tanh X}{{\coth }^{2}X}+\frac{{\mathrm{sech}}^{2}X\tanh X}{{\coth }^{2}X}$

$\frac{{\sinh }^{4}X+\left({\cosh }^{2}X+1\right){\sinh }^{3}X}{{\cosh }^{5}X}$

$\mathrm{DONE}$

$-\frac{i\left(e^{iX}-e^{\left(iX\right)}\right)}{2}$

$1-\frac{X^2}{6}+\frac{X^4}{120}+\text{⋯}$

$2{\cos }^{2}X-1$

${\left(2i+1.5\right)}^2$

$6.0i-1.75$

${\left(1\right)}^{\frac{1}{4}}\sqrt{2}$

$\mathrm{DONE}$

$\cos Y+\sin X+\frac{d}{dW}\sin W+{\left(W+1\right)}^2$

$Y+A+2$

$\frac{d^3}{d{X}^{2}dY}\left(Y^2+XY+X^2\right)$

$0$

$2X-3Y=3$

$2Y-3X=-4$

$\left[\left[Y=\frac{1}{5},X=\frac{6}{5}\right]\right]$

$3=3$

$X+\frac{1}{X}>\sqrt{\pi }$

$\mathrm{true}$

$\mathrm{true}$

$\mathrm{false}$

$\mathrm{DONTKNOW}$

${\left(\frac{1}{{\left(Y+X\right)}^4}-\frac{3}{{\left(Z+Y\right)}^3}\right)}^2$

$-\frac{6}{{\left(Y+X\right)}^4{\left(Z+Y\right)}^3}+\frac{9}{{\left(Z+Y\right)}^6}+\frac{1}{{\left(Y+X\right)}^8}$

$A\cdots F+A\cdots C\cdots E+A\cdots C\cdots D+A\cdots B$

$X^3+3X^2+3X+1$

${\left(X+1\right)}^7$

$X^7+7X^6+21X^5+35X^4+35X^3+21X^2+7X+1$

$X^7+7X^6+21X^5+35X^4+35X^3+21X^2+7X+1$

$A{\left(C+B\right)}^2+AC+AB$

$-27Y^3+54X{Y}^2-36X^{2}Y+8X^3$

$\frac{X-1}{{\left(X+1\right)}^2}+\frac{1}{X-1}$

$\frac{X}{X^2+2X+1}-\frac{1}{X^2+2X+1}+\frac{1}{X-1}$

$\frac{2X^2}{X^3+X^2-X-1}+\frac{2}{X^3+X^2-X-1}$

$\sin \left(\frac{X}{X^2+X}\right)=e^{{\left(\log X+1\right)}^2-{\log }^{2}X}$

$\sin \left(\frac{1}{X+1}\right)=e{X}^2$

$BX+B\left(\frac{A}{B}-X\right)+A$

$2A$

$\frac{{\left(X-1\right)}^{\frac{3}{2}}-\sqrt{X-1}\left(X+1\right)}{\sqrt{X-1}\sqrt{X+1}}$

$-\frac{2}{\sqrt{X+1}}$

$X^{\frac{A^2+1}{A}}$

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

${\left(\log \left(X+1\right)\right)}^{\frac{A}{2}}$

$\frac{\log \left(A^{2X}+2A^X+1\right)}{\log \left(A^X+1\right)}$

$2$

$\frac{e^X-1}{e^{\frac{X}{2}}+1}$

$e^{\frac{X}{2}}-1$

$\mathrm{DONE}$

$\frac{B+A}{Y}+\frac{B+A}{X}$

$-\frac{1}{X-Y}+\frac{X}{{\left(X-Y\right)}^2}-\frac{F\left(X\right)}{{\left(X-Y\right)}^3}$

$-{\left(X-Y\right)}^2+X\left(X-Y\right)-F\left(X\right)$

$-Y^2+XY-F\left(X\right)$

$\frac{{\left(B+A\right)}^{10}{S}^2+2ABS+A^2{B}^2}{AB{S}^2}$

$\frac{2}{S}+\frac{AB}{S^2}+\frac{{\left(B+A\right)}^{10}}{AB}$

$A\cdots F+A\cdots C\cdots \left(E+D\right)+A\cdots B$

$\frac{1}{{\left(Y+X\right)}^{19}}+\frac{{\left(X+2\right)}^{20}-2Y}{{\left(Y+X\right)}^{20}}-\frac{X}{{\left(Y+X\right)}^{20}}$

$\frac{{\left(X+2\right)}^{20}-Y}{{\left(Y+X\right)}^{20}}$

$\frac{2}{X+2}-\frac{2}{X+1}+\frac{1}{{\left(X+1\right)}^2}$

$-\frac{X}{X^3+4X^2+5X+2}$

$\frac{2}{X+2}-\frac{2}{X+1}+\frac{1}{{\left(X+1\right)}^2}$

$7^{2}7312733792737649657$

$\left(2Y+X\right)\left(Z-2\right)\left(Z+2\right)$

$X^2{Y}^2+2X{Y}^2+Y^2-X^2-2X-1$

$\frac{\left(X^2+2X+1\right)\left(Y-1\right)}{36\left(Y+1\right)}$

$\left(e^X+1\right)\left(e^{2X}-e^X+1\right)$

$\left(X^2-AX+1\right)\left(X^2+AX+1\right)$

$-\left(Y^2+X\right)\left(Z-X\right)\left(Z+X\right)$

$\frac{X+2}{\left(X+3\right)\left(X+B\right){\left(X+C\right)}^2}$

$\frac{X+2}{X^4+\left(2C+B+3\right)X^3+\left(C^2+\left(2B+6\right)C+3B\right)X^2+\left(\left(B+3\right)C^2+6BC\right)X+3B{C}^2}$

$-\frac{C^2-4C-B+6}{\left(C^4+\left(2B-6\right)C^3+\left(B^2+12B+9\right)C^2+\left(6B^2-18B\right)C+9B^2\right)\left(X+C\right)}-\frac{C-2}{\left(C^2+\left(B-3\right)C+3B\right){\left(X+C\right)}^2}+\frac{B-2}{\left(\left(B-3\right)C^2+\left(6B-2B^2\right)C+B^3-3B^2\right)\left(X+B\right)}-\frac{1}{\left(\left(B-3\right)C^2+\left(18-6B\right)C+9B-27\right)\left(X+3\right)}$

$-\frac{C^2-4C-B+6}{{\left(C-3\right)}^2{\left(C-B\right)}^2\left(X+C\right)}-\frac{C-2}{\left(C-3\right)\left(C-B\right){\left(X+C\right)}^2}+\frac{B-2}{\left(B-3\right){\left(C-B\right)}^2\left(X+B\right)}-\frac{1}{\left(B-3\right){\left(C-3\right)}^2\left(X+3\right)}$