> #sfb 20 Nov 2001
> #From Project
> assume(r>0);Int((4/3)*Pi*(r^2-x^2)^(3/2),x=-r..r)=int((4/3)*Pi*(r^2-x^2)^(3/2),x=-r..r);
> 
> with(plottools);with(plots):
> ?torus
> ?polygon
> level:=0;
> T:=torus(color=green):P:=polygon([[3,3,level],[-3,3,level],[-3,-3,level],[3,-3,level]],color=blue):
> display([T,P],scaling=constrained);
> ?cylinder
> ?plottools,cylinder
> C:=cylinder([0,0,0],1,2*Pi*2):P2:=polygon([[level,-2,0],[level,2,0],[level,2,4*Pi],[level,-2,4*Pi]],color=blue):
> display([C,P2],scaling=constrained);
> display([C,P2,T,P],scaling=constrained);
> ?transform
> S:=transform((x,y,z)->[y+4,z-2*Pi,x]);
> display([S(C),S(P2),T,P],scaling=constrained);
> #first guess x e^x
> diff(x*exp(x),x);
> diff(x*exp(x)-exp(x),x);
> diff(x*exp(-2*x)/(-2),x);
> diff(-exp(-2*x)/4,x);
> diff(x*exp(-2*x)/(-2)-exp(-2*x)/4,x);
> diff(x^2*exp(x)-2*x*exp(x)+2*exp(x),x);
> diff(x*sin(x)+cos(x),x);
> diff(x*ln(x)-x,x);
> diff(x*arctan(x)-ln(1+x^2)/2,x);
>