The need to take calculus and other math related classes in an engineering or science field is not to know how to solve integrals or differential equations in your mind for a normal 9to5 job, but it's for something extremely important in computer science an engineering in general: abstraction; the ability to, when faced with a [new] problem, hide the details away for a moment and concentrate on the important parts, recognize patterns, know which tools to use, etc. Then you can go bringing back the details when you need them, to form a solution.
You'd certainly go crazy if you start to think in all the little details as soon as you face a problem, and probably never deliver a solution on the time needed.
It turns out that mathematics are very good at, gradually, giving you new levels of abstraction to solve new problems, or old problems in new ways, etc. The important is not to memorize formulas (that's what books and wikipedia are for), but to know which one to use, and when, their uses, etc.
You'd certainly go crazy if you start to think in all the little details as soon as you face a problem, and probably never deliver a solution on the time needed.
It turns out that mathematics are very good at, gradually, giving you new levels of abstraction to solve new problems, or old problems in new ways, etc. The important is not to memorize formulas (that's what books and wikipedia are for), but to know which one to use, and when, their uses, etc.