> # sfb modified from 7 Mar, 2002
> with(plots):with(plottools):with(linalg):
> x=r*cos(theta);y=r*sin(theta);
> coordplot(polar,color=[red,black],scaling=constrained);
> a:=polarplot(1+cos(theta),theta=0..2*Pi,scaling=constrained,color=blue):
> b:=plot({x,x/sqrt(3)},x=-0.5..2,color=green):
> c:=polarplot({1, 1.2},theta=0..2*Pi,color=green):
> display(a,b,c);
> # dA = dx dy = r dr dtheta
> 
> time(int(int(1,y=-sqrt(1-x^2)..sqrt(1-x^2)),x=-1..1));
> time(int(int(1*r,r=0..1),theta=0..2*Pi));
> time(int(int(sqrt(1-x^2-y^2),y=-sqrt(1-x^2)..sqrt(1-x^2)),x=-1..1));
> time(int(int(sqrt(1-r^2)*r,r=0..1),theta=0..2*Pi));
> # cylindrical coordinates (r, theta, z) [Polar with z]
> x=r*cos(theta);y=r*sin(theta);z=z;
> coordplot3d(cylindrical);
> coordplot3d(spherical);
> a:=sphereplot(2,theta=0..2*Pi,phi=0..Pi/4,scaling=constrained):
> b:=cylinderplot(z,theta=0..2*Pi,z=0..sqrt(2)):
> display(a,b);
> #dV = rho^2 sin (phi) d pho d phi d theta
> 'int(int(int(rho^2*sin(phi),rho=0..1),phi=0..Pi),theta=0..2*Pi)'=int(int(int(rho^2*sin(phi),rho=0..1),phi=0..Pi),theta=0..2*Pi);
> 'int(int(int(1*r,z=-sqrt(1-r^2)..sqrt(1-r^2)),r=0..1),theta=0..2*Pi)'=int(int(int(1*r,z=-sqrt(1-r^2)..sqrt(1-r^2)),r=0..1),theta=0..2*Pi);
> 'int(int(int(1,z=-sqrt(1-x^2-y^2)..sqrt(1-x^2-y^2)),y=-sqrt(1-x^2)..sqrt(1-x^2)),x=-1..1)'=int(int(int(1,z=-sqrt(1-x^2-y^2)..sqrt(1-x^2-y^2)),y=-sqrt(1-x^2)..sqrt(1-x^2)),x=-1..1);
> x=rho*sin(phi)*cos(theta);y=rho*sin(phi)*sin(theta);z=rho*cos(phi);r=rho*sin(phi);
> restart;
>