Trott-Strzebonski method for In-Place Evaluation

One of the all-time cleverest idioms I've seen; this was discovered by Michael Trott and Adam Strzebonski a few years ago.  The template is a rule of the following form:

   lhs :> With[{eval = lhs}, eval /; True]

Suppose you want to replace a bunch of things inside a held expression, and have the replacements evaluate.  You don't want to evaluate the whole, just the pieces that are targeted.

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You can also do this with ReplacePart, but it's harder to code, and has a worse time and space complexity for a large number of substitutions (and using Fold with ReplacePart would be O(n^2)).