> f:=4*x+3*y;g:=x^2+y^2-25;
> F:=f-lambda*g;
> diff(F,x);diff(F,y);diff(F,lambda);
> ans:=solve({diff(F,x)=0,diff(F,y)=0,diff(F,lambda)=0});
> subs(ans[1],f);subs(ans[2],f);
> with(plots):a:=implicitplot(g,x=-6..6,y=-6..6):b:=contourplot(f,x=-6..6,y=-6..6,color=green):display(a,b);
> a:=implicitplot(g,x=-6..6,y=-6..6):b:=contourplot(f,x=-6..6,y=-6..6,color=green,contours=[-25,-15,-5,5,15,25]):display(a,b);
> f:=x+y+z;g:=x^2+y^2+z^2-1;h:=x-y-1;
> F:=f-lambda*g-mu*h;
> diff(F,x)=0;diff(F,y)=0;diff(F,z)=0;diff(F,lambda)=0;diff(F,mu)=0;
> 1-2*lambda*y+mu = 0;
> ans:=solve({diff(F,x)=0,diff(F,y)=0,diff(F,z)=0,diff(F,lambda)=0,diff(F,mu)=0});
> ans2:=allvalues(ans);
> subs(ans2[1],f);subs(ans2[2],f);
> implicitplot3d({g,h},x=-1..1,y=-1..1,z=-1..1);
> #integrals.
> int(int(x^2,x=y..1),y=0..1);
> int(int(x^2,y=0..x),x=0..1);
> int(int(ln(x),x=exp(y)..exp(1)),y=0..1);
> int(int(ln(x),y=0..ln(x)),x=1..exp(1));
> implicitplot({y,y-x,x,x-1},x=-1..2,y=-1..2);
> implicitplot({x-exp(y),x-exp(1),y,y-1},x=0..4,y=-1..2);
> f:=GRID(0..1,0..1,[seq([seq(i+j,j=1..10)],i=1..5)]);
> PLOT3D(f);
> a:=plot3d(x+y,x=0..5,y=0..10,style=wireframe,color=blue):a;
> with(plottools):
> f:=seq(seq(cuboid([i,j,0],[i+1,j+1,i+j]),j=0..9),i=0..4):
> display(f);
> display(a,f);
> 'int(int(x+y,y=0..10),x=0..5)'=int(int(x+y,y=0..10),x=0..5);
> Int(Int(x+y,y=0..10),x=0..5)=int(int(x+y,y=0..10),x=0..5);
>