Hello Ash Ash,
Perhaps I misunderstand your question. I am assuming that you are no longer interested in a maxima.
To find the value of an expression for a particular value of a parameter, you can use slash-dot with a rule:
expr = a Cos[ b x]
expr /. a -> 2
expr /. {a -> 2, x -> 3}
expr /. {a -> 2, b -> 3, x -> Pi}
More information can be found here: tutorial/ApplyingTransformationRules