Speaking from experience, most of it doesn't.
However, most computer science departments appear to want their CS degree holders to have at least a working knowledge of calculus. If you want a CS degree but don't want to deal with calculus, you may be able to find a school without the math requirement — but beware that this may decrease the value of the degree.
As for engineering? Calculus pops up in all kinds of things, and if you have no knowledge of calc you can just find yourself lost when looking at all kinds of real-world problems.
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