What would be really useful is a calculator that has natural display, i.e. leaves answers as surds, fractions etc for ultimate precision and easier readability.

It needs a symbolic math engine, otherwise sqrt(4)-2 will never be evaluated to 0. It can be done, but similar algebraic simplifications are very hard. Rational display is possible, too, but again, what would you expect to see for sqrt(2)? 14142/10000 or 1.4142. It could be a very interesting project, but probably too large for AHK.

graphing functions are a must.

They are more realistic, especially, since jonny already posted the necessary code. I will look into it.