Why is it lazy to use the best tool for the job? It's not as if the computer program can tell you if you input the correct equation.

I can multiply very large numbers in my head, but if I have a calculator on hand, I'm using it. Once I've set up an integral, you can bet I'm going to use software to solve anything but the most uselessly fundamental stuff. Same goes for eigenvectors and eigenvalues. Some stuff is just busy work that a computer can solve instantly, which lets you use your mind for things the computer can't do.