In Maple, how can I compute int(exp(- c*r^2), r= 0..infinity) without assigning a numeric value to c?

In Maple, the integral converges or diverges depending on the value of  c . You need to tell Maple a bit more about it before it will answer. See the following examples:

This returns a "prettyprinted" form of sqrt(Pi/c)/2. In the output, the variable  c  will have an appended tilde (~) to indicate that it carries assumptions. If instead you use the following, it will return infinity:

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