If you manage to write a program that calculates definite integrals using Windows APIs, then... wow. That would be amazing, and maybe the judges would see that.
What would also be really impressive is if you created a Mathematica-like program WITHOUT using yacc or bison. O_o
Yacc and Bison are parser generators. A parser is a grammar-evaluator (sort-of). You feed it a string of tokens and the original text, and it does shtuff with it.
There are no parsers in the standard C++ library, and it is ridiculously tedious to create a parser for such a language from scratch. That said....
Finding indefinite integrals requires symbolic computation. It's much more complex than just evaluating an expression at regular intervals.
Don't bite more than you can chew, is what I say.
Making something that introduces advanced mathematical algorithms in OpenGL. Like, for instance, some refraction. Something that makes something more realistic than usual.
I don't think it would hurt if you liked math, but it probably won't be a big issue unless you want to study theoretical computer science or work on projects that required a working knowledge in one or more areas of mathematics. I'm working on a mobile robotics project at the moment, and control theory, matrices and trig seem to pop up a lot.