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Question: How to introduce a binary operation containing an unknown function?

Question:How to introduce a binary operation containing an unknown function?

zviadk1969 5 Maple
procedure associativity
July 12 2019
1
I need to set up in Maple the following binary operation $*$:

where $Q$ can be chosen to be a specific function (linear, polynomial, exponential or any other elementary function) of its input, while $\phi$ is kept the way it is (just "some function of $u$").

The main purpose of this Maple exercise is to check associativity of operation $*$ for various choices of $Q$.
Without $\phi$ (or $\phi$ being an identity map), I think I could check the associativity of $*$ with basic Maple syntax.  But keeping $\phi$ unknown makes it confusing.  Any advice on how to introduce this operation in Maple?
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