Repair broken desk lamp
I'd suggest some plastic cement from a hobby shop (different from CA/superglue). The good stuff will glue the plastic, but will not stick to your fingers.
If you've got all the pieces, you should be able to hold the plastic together to make a nice tight seam, then you dab a bit of glue on with a small paint brush. The glue sucks into the joint and chemically welds it. If you're holding it right, you should be good to go.
Take your time and be patient and there's a high likelihood that you'll never see the seams. While you're at the hobby shop, take a look at the plastic models they've built using this stuff - most likely you won't see seams in it, either.