RE: cougars in illinois?
I'll tell you what I was told. It was second or third hand so it'd be a good idea to check with the DNR yourself.
We've got some here locally (central Pike county near Perry Springs) that attacked my wife's aunts Emu's. My father-in-law contacted the DNR and found out they knew there were cougars running around. He was also told that if you shoot one you have to leave it lay until a DNR CO sees it and says it's ok to do whatever you want to with it.
There should be more dots on that map above, but I guess the reports I've been told never made it to who keeps it updated.