Answer: Maple trees are relatively shallow-rooted. If you cover the roots, you risk "smothering" the tree. I would place no more than an inch of soil over the roots; if that won't cover them, then perhaps you can set a park bench over the worst ones, or something like that to keep people from tripping over them. I wouldn't put anything large there that will affect how water gets to the roots, or anything that limits air circulation.
I wouldn't plant a flower bed, but you could try to establish a durable ground cover (by covering the area with just that inch of soil). You'll need to remove the existing grass, but don't till or you could damage the shallow tree roots. (Ajuga, pachysandra, or periwinkle would be good ground cover choices.)
Enjoy your new yard. How about a swing off one of those low branches--I can almost feel the breeze in my face!
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