Read more about advanced searches: http://www.rememberthemilk.com/help/answers/search/advanced.rtm

Be sure also to read about Smart Lists; searching and Smart Lists are pretty much the backbone of RTM's power.

There are a lot of different tips on the forums about how to create interesting lists to capture just the tasks you want to see at any given moment; feel free to peruse, or just post back if you have any questions!

I read about the smart lists and the search terms you can use. I just don't see a way to use the advanced search and use any date term besides "due date within", the way the boxes are set up.

I did find I could type anything I want in the small search box and hitting return afterward.

jstaso,
Absolutely, the search boxes will only get you so far. For the two examples you mentioned, you won't be able to use them.