Being able to do calculus helps you think critically and serves as a basis for study in many other important fields. There's a pattern of reasoning skills that you develop when you read a book, learn a method, apply it to solve a problem, verify your answer, and return to the problem to identify and correct errors.

Being able to solve the problem without having to look it up gives you an intuition for solving complex problems without having to resort to such means. If I tell you the derivative of a value is x^{-1}, you shouldn't need to look up that it varies logarithmically. And being able to solve the problem yourself is what gives you the faith in the solution being correct. You could always look up the wrong value from the table, or provide the wrong input to a compute engine (side rant: Mathematica syntax drives me bonkers). You should always have multiple ways of *understanding* and verifying your solutions because relying solely on existing tools to perform the work for you without understanding where they come from turns this process into a black box which you have to rely on purely out of faith; I would argue that this can be dangerous, especially for mission critical applications. For basic calculus, linear algebra and differential equations, which every college engineer is expected to understand, I don't think this is an unreasonable requirement.

Even while you yourself may have not been in a situation where you needed to understand these concepts, there are many fields in which being able to manipulate these equations is important: particle advection, comupter graphics and animation engines (manipulating ODEs and PDEs, linear algebra), or scientific and numerical computing and modeling (pretty much anything field of math). So I would say, if I were developing a comprehensive computer science program, I absolutely would have to include this in my curriculum, otherwise I would be shutting our students out of these fields. And if you're a mechanical, electrical, chemical, etc. engineer (or you're any other kind of engineer having to work with them), you need to understand these concepts to have faith in your results.

The purpose of your college program was not to cater its curriculum directly to you, but to give all the students enrolled a broad set of skills that they could apply in situations that might arise. And understand that your program can only expose you to the skills that you should learn, but it's up to you to find a practical use for them.