Answer: Black plastic mulch is suggested for crops that like warm soil (melons, squash, corn, tomatoes, peppers, cucumbers, pumpkins). It's not a good idea to use it where summers are extremely hot and sunny, or the roots may not survive. It's often used to warm up the soil in early spring to get an early start on the season.
If you leave it on the soil, you need to ensure that irrigation flows under the mulch, or leave large planting holes in the mulch, so you can water the plants. Some cool-season crops (such as peas) cease to produce when their roots get too warm. You can use it to warm the soil early in the season, but mulch over it with organic matter on your cool-season crops as the season heats up.
I think in your climate it's a toss-up between leaving the plastic on or taking it off. On the one hand, it warms up the soil; on the other it can make watering more difficult, and nutrients from the organic mulch as it breaks down won't move as freely through the soil.
You can try to reuse the plastic, but it may not be in very good condition. Some gardeners prefer black landscape fabric--it's more expensive, but it will last longer than plastic, and allow air and water to reach the soil.
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