A few corrections: The + (formerly used to force a term to be present in the result) and ~ (also find synonyms) operators have been deprecated. Google now advises to wrap the word in quotes instead of using the +. Google will also automatically look for synonyms without the use of ~. I have seen 'AROUND(n)' mentioned in many other places working as a proximity operator in Google, but I don't believe that is true and…
The plus operator in the page appears to be binary rather than unary. I've never used it. Is that affected as well? (Though I'm confused why AND is necessary. Isn't it implied normally?)
It's a little confusing because fo how Google implemented some of the operators. The boolean + operator in many cases is used in the same way as AND, but Google originally used it to let users to force a specific word to be present in a search result.
So a search for Fish +Chips was a search for both words, but 'Chips' MUST be present. The equivalent search today is Fish "Chips". It's a little annoying because it requires typing another character, and it it is still not always respected.