image-area + camera (camera on right lower-right(or left)-hand side)
I tried adding both of those together and there is just far too much detail to try to fit in one icon. Does something simplified like this work for your needs?

Yes, please. But if possible, could the plus be a camera?
I believe that replacing the camera with a plus would be too small and unrecognizable. I believe what @casesandberg has done works great.
@casesandberg we'll need a zip file with the svg.
What should we name this icon?
crop + select
select + rectangle
????
Maybe select-area.
Could we use the select icon as the base and have a plus and minus variant? Would be useful for tools that add to or remove from an existing selection.
In Android P there's a new screenshot icon in the power menu:

@PeterShaggyNoble Good point, might be a good idea to create icons for monitor and laptop too.
In Premiere Pro there's an option to export a frame, which uses a camera symbol.
The Windows Snipping tool uses a scissors symbol and some random circle.
Other common symbols:


Most helpful comment
I tried adding both of those together and there is just far too much detail to try to fit in one icon. Does something simplified like this work for your needs?