Have you seen the ! queries on DuckDuckGo? If you add !g to a search, it redirects you to Google. !i goes to Google Image search. I guess there are others.
More complex queries are typically done with Wolfram|Alpha. This goes a long way: https://duckduckgo.com/?q=graph+y+%3D+x%2Bcos^2%28sqrt%2842*...