Shade-tolerant veggies?

The bottom-right corner of the garden in this photo is the southeast corner of the garden. It was taken at about 11 a.m. I didn't notice the shade from this tree until I started planting, and I put the snow peas and lettuce in the bottom-right corner because it seemed to be in shade the longest and significantly cooler.

The middle area to the left before you get to the strawberries - the green portion in the middle - seemed to be in shade the longest during the day. Maybe a couple of hours, at least. So what should I plant there? I think I read that cucumbers can take some shade. Other than that? Maybe just flowers? (I already put the broccoli and pac choi in what will be the shade of the potatoes.) Suggestions?

I grow bush beans in a spot just like that. They do exceptionally well. They get the least sun of anything in my garden.
I haven't found anything else that out performs the beans. I also have had some success with carrots in the same bed. But, to be fair, I planted the carrots later than the beans so they were not given an even playing ground. By late fall, this area is really short on sun, but the beans keep going until frost.

Really? I'm nervous about the beans (normally obnoxiously prolific) because my pumpkins crowded them out last year and the Japanese beetles stressed the poles. Probably right, though. I could put some in full sun and some in part shade and see what happens.

I think you should try it out.
As a matter of fact, I am growing bush beans this year in all spots that get less sun. Just because they do so well. I would say that pole beans need full sun. My pole beans have not done well in spots without it.
I have tried a lot of combinations over the years in that shady spot. I even did half runner beans last year in that part sun bed and they excelled.
So, I would say at least experiment with part of that space.
I never would have believed it either. And I am in Maine. LOL

I'm glad you said it because I wouldn't have guessed it.

And Maine, good point. It's a heck of a lot different than part shade in TX.