Here is my worksheet code:

> f := theta -> (a*b)/sqrt(a^2*(sin(theta-Pi/4))^2+b^2*(cos(theta-Pi/4))^2)+c*cos(4*theta);

(1) ...

> simplify(f(theta));

(2) ...

 > subs(sqrt(a^2*(cos(theta+Pi/4))^2+b^2-b^2*(cos(theta+Pi/4))^2)=tmp,simplify(f(theta)));

(3) ...

<p>I apologize if this seems quite basic, but that's the point where I am in learning about Maple.  I would like to define a function, take its derivative, plot it, divide it by its derivative, plot that result, etc...</p>
<p>For example: f(x) = a*x^2 + b*x + c</p>
<p>From what I've learned so far, I think I do this to define the function:</p>
<p>f := x -> a*x^2+b*x+c</p>
<p>I also seem to have learned that:</p>
<p>diff(f, x)</p>
<p>doesn't do what I want, but</p>
<p>diff(f(x),x)</p>

Actually, I could just cut to the chase here...

I need to print out a 2-D ring and then attach that to a 3-D sphere.  The problem is that the 2-D ring will buckle as I attempt to attach the outer circumference of it to the sphere.