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And the ideal application of those existing solutions often requires creativity to mate them to the problem domain.

Is an artist not creative if they use pre-mixed paint?

A more apt analogy would be asking if an artist isn't creative because they put a jigsaw puzzle together.

A jigsaw puzzle goes together only one way. Many engineering problems can be solved in infinitely diverse and creative and unique ways.

put the jigsaw together by haphazardly cutting off all the tabs that wouldn't lie flat and filling in all the empty spaces with glue

That is called learning and is indeed a creative process.