What environment should I use if I just want to test different math things?

For example, I've asked about the breakout formula to calculate the ball bounce. Inside of XNA, I don't know where I would code this and to even display something I would need a lot of code.

Is there something simple to visualize math formulas such as the one above?

I asked something like this some time ago in Stackoverflow.com and the answers are pretty good.

I ended up using Octave and it was awesome.

I tend to reason through problems on plain old pencil and paper. There's just nothing quite like it; it's completely unstructured.

Otherwise, I mean, there are math problems like Maple, Matlab or Mathematica (those are the popular three) but they of course have a learning curve.

Figuring out that particular problem was mostly just a matter of reasoning; define exactly what you want to accomplish, what variables you need (intersection point, velocity of ball, distance of intersection from center of paddle, minimum and maximum speeds), and then determine how to go from what you have to what you want.

Sometimes maybe it just takes being familiar with the math too, or having solved similar problems or understanding different angles of the problem. For example, I had already seen similar problems like this one in my Calculus classes, so it was pretty easy for me to tackle. Math is important in game development.

If you're up for learning a new language, the R language is designed specifically for visualizing pure math.

Processing.js is another language geared toward visualization.

You can use MatLab, but I personally dont.

Whenever I want to type out a bunch of quick code to test a formula, I actually use the python interpreter. Python is great for something like this, and running something in the interpreter is really quick and easy.