@acer Okay, I agree. I had tested it earlier by mapping the simplify. But it doesn't work if I map the simplify and include the assuming, even though that works for functions other than Int. I'm branching it off to a separate Question.

Do you have any idea what the simplify does in your Cartesian-coordinates integral? I noticed that if I apply simplify to the integrand (after the inner integration is done), the integrand is changed slightly, but the integral still returns unevaluated.

Do you have any idea what the simplify does in your Cartesian-coordinates integral? I noticed that if I apply simplify to the integrand (after the inner integration is done), the integrand is changed slightly, but the integral still returns unevaluated.

@Preben Alsholm I see my mistake now! It's -2*y, not -2*x*y.

@Preben Alsholm I see my mistake now! It's -2*y, not -2*x*y.

My Maple 17 does not have the command dividend.

But along the same lines there is

evalindets(y=a*(b-c), `+`, x-> b*expand(x/b));
                                /    c\
                        y = a b |1 - -|
                                \    b/

My Maple 17 does not have the command dividend.

But along the same lines there is

evalindets(y=a*(b-c), `+`, x-> b*expand(x/b));
                                /    c\
                        y = a b |1 - -|
                                \    b/

Why do you ask? Is it because you have an system of ODEs that you think would be best solved by one of those methods? Is it because you want to study the method? Or is it some other reason?

@Markiyan Hirnyk Markiyan, do you have a specific question about my code? Perhaps it would help to say that my V is not a Vector; rather, it is a procedure which returns a Vector. In particular, it returns a numeric Vector when passed a numeric argument.

The code

V||(1..4):= 'V(k)' $ 'k'= 1..4;

does exactly the same thing as

(V1, V2, V3, V4):= seq(V(k), k= 1..4);

@Markiyan Hirnyk Markiyan, do you have a specific question about my code? Perhaps it would help to say that my V is not a Vector; rather, it is a procedure which returns a Vector. In particular, it returns a numeric Vector when passed a numeric argument.

The code

V||(1..4):= 'V(k)' $ 'k'= 1..4;

does exactly the same thing as

(V1, V2, V3, V4):= seq(V(k), k= 1..4);

@Markiyan Hirnyk Did you have in mind a 3D plot in cylindrical coordinates?

I tell calculus III students that to plot a surface over a region in the xy-plane, use plot limits that are the same as the limits of integration that you would use for double integral over that region.

I tell calculus III students that to plot a surface over a region in the xy-plane, use plot limits that are the same as the limits of integration that you would use for double integral over that region.

You said that Eigenvalues(M) returns 17 eigenvalues. Are any of those 17 expressed in terms of the parameter x?

@vshyam But I am still curious to know: Do you have an integral for which Maple's default quadrature routines failed? Perhaps some tweaking of the optional parameters to Int is all that is needed. See ?int,numeric.