Answer: None of the vegetables commonly grown in gardens want to be in the shade all day. If there is anything you can do to brighten the light intensity in the area, it would really help the garden. Short of removing some trees, trimming lower limbs and selective removal of some limbs in the upper canopy can help brighten an area.
Among the more shade tolerant vegetables are the leafy greens like lettuce, chard and mustard. The cole crops (broccoli, cauliflower, kohlrabi and cabbage) are also somewhat tolerant of lower light levels. Fruiting crops and most root crops on the other hand will not produce well in shady spots.
Hope this helps!
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