Now that we have that settled, there's another humidity-related factor to consider: Condensation when static pressure drops (for example, at Vr on a very humid day). A cloud forms over the wing - you see it a few dozen times an hour at ATL or MIA or other steamy burgs.
That same cloud forms inside the inlet of a jet or fan engine, and the condensation has a side-effect: The
heat of condensation increases the air temperature a few degrees. The engine behaves just as you'd expect - a bit lower output because of reduced density.
To simplify the aircraft performance, this is already accounted for in your AFM performance charts. Thus, if you take off in a very dry desert condition, your actual performance will be a bit better than book, since there's no condensation to worry about.