Talking about Maxima...



I've let myself in to giving a little introductory talk to my department
about Maxima.  When I say "talk", rather than a slides-based seminar, I
intend it to be more of a demonstration, where I shall show a few of
Maxima's capabilities.

Now, many people in my department use Maple, and a few have used
Mathematica, and so I'd like to be able to compare Maxima to these two
products.   Does anybody know:

   1. are there any "simple" problems which one would expect Maxima to be
   able to solve, but which it can't?
   2. is there any functionality in which Maxima is better than its
   rival?
   3. Aside from price and its being open-source, what are the greatest
   strengths of Maxima?

Now, I can probably give rough answers to these myself, but it's always nice
to garner other views and opinions.

Thanks,
Alasdair