Hey, People With Dogs! How Do I Fix These Stupid Holes?

Yeah, I know what it's shaped like. And please don't tell me "put some dirt in it". I need some serious advice on how to repair several holes in my backyard dug by a very determined dog.

The picture doesn't really do it justice.....it's almost a foot deep and a couple feet long. Pouring dirt in there and stomping it down doesn't seem like it would last through a good rainstorm.

What's the best way to fill/repair/regrow these unsightly and dangerous holes? Need your help!