I've had considerable difficulty in integrating products of trig functions with Maple. It usually expands the trig functions into forms that just are a mess to deal with. So, I usually handle this by splitting an expression into two parts: a constant term that doesn't depend upon the integration variable and a dependent term. In the past, I've usually done this by hand but have now created a procedure to do this automatically.
I'd really like better linear algebra support. I've been wanting some features that have been in Mathematica now for several years. I'd really like to be able to write out,
where c is a vector and B is a matrix without having to specify their size other than they are conforming. Then be able to manipulations on them such as differentiate with respect to c. I know that Mathematica can do this, and the lack of this support makes doing my work difficult. I had to do a lot of work to get around this problem when creating my symbolic finite element package.
The other major thing that I've complained about before including in various places on Mapleprimes (but not in the suggestions forum) is better LaTeX export.
I've been completely unsatisfied with the Maple LaTeX output. So, with the help of Joe Riel on comp.soft-sys.math.maple, I've created a procedure to use instead of a call to the latex command called simpleLaTeX. I've attached to this entry a Maple 9.5 worksheet that contains the procedure and a sample of its use. I'd appreciate any feedback people might have or further suggestions. Please send me any modifications you might make to the procedure. It seems to work quite well for all the test expressions I've sent to it.