I always plant my mid and late summer arugula in the shade. It does get morning sun though. Grows very well under the east side of the oak tree. My cucumber also do well in that location, but would think that they would need to get a few hours of full sun to produce well. Might be worth an experiment, might surprise you.
I've researched this because I'm planning a partial shade garden for next year:
asparagas
currants
raspberries
mint
strawberries
pak choi
lettuces/lettuce crops like raddiccio, arugula, etc
spinach
chives
parsley
I've not personally grown any of these in sun or part shade, but am planning on it. A good resource for me was the book, "All in one Garden" by Graham Rice.