I have found the following use of the word "evaluate" in several math books:
"To evaluate the continued fraction, start at the bottom and work your way up:"
$\huge \underbrace{2 + \frac{1}{1+\frac{1}{3}}}=2 + \frac{1}{\frac{4}{3}}=2+\frac{3}{4}= \underbrace{\frac{11}{4}}$ Why is this called an "evaluation" and not a simplification?
Because people commonly use the word evaluate in that context; this is simply a fact of usage. You can see other examples here on the website of the National Institute of Standards and Technology, in the title of this paper in SIAM Review, and here, to pick three of the first few examples that turned up on a search. In this context evaluate simply isn’t the technical term whose definition you give in the comments; it’s another sense of the same word.