I do chemical engineering research in my spare time. I actually had to use calculus a few weeks ago to derive an equation for making a mixture of 2 solvents as similar as possible to the properties of a third solvent. For two solvents, the answer was a calculus gimme.
For three solvents, I had to break out multivariable calculus and Lagrange multipliers which didn't generate a solution but instead reduced the problem to a 4x4 matrix inversion. The inversion would have been most easily solved by feeding the matrix into the LAPACK library but a pedant could have solved it in his own code using Cramer's rule.
In my case, calculus wasn't enough, it only reduced the problem to linear algebra. Basically, you have to have taken enough math to recognize when you have transformed a problem form an intractable form to a tractable form.