[candiodari]

This is the sort of thing that reviewing other people's performance can really help with. Offer to teach classes, grade homework, or whatever.

Second thing that helps me pretty well is doublechecking through another path. You know, figure something like this out, check if the angles of the triangle still add to 180, check if substracting half the equation from the previous step still yields the same, that sort of thing. For the problem you said, find an "easy" definite integral that is easy to calculate (e.g. a sine is 180 degrees of the unit circle, so integral(0,1,x->sinx) is p/4).

So take a "trivial application" of the mathematical expression (like calculating the area of the unit circle), and execute it on every step, calculating what should be the area of the unit circle. As long as you replace expressions with equivalent expressions the outcome should stay the same.

And for coding, unit tests, but more than that, running the code, using a debugger or so.