USA _ I think at or under 49 ccs and you're golden. obey traffic rules of course.
There's a little more to it than that.
Most state laws define bicycles as being powered solely by human power. If it has any kind of motor or engine on it, even if it's not running, it's no longer a bicycle.
The word "moped" means "MOtor and PEDals". Mopeds are defined by most states as having no more than 50cc AND no more than two horsepower AND a top speed of no more than 30 mph on flat ground.
But his has more than 50cc, so it's not a moped either. It's a motorcycle. And in most states, you need motorcycle drivers license, motorcycle insurance, license plate, registration, and all of the DOT-legal road equipment that any other motorcycle is required to have- low and high beam headlights, blue high beam indicator, speedometer, odometer, horn, tail light, brake light, license plate light, muffler, front and rear turn signals, DOT-approved tires, fenders, and so on.
The big ones are no motorcycle insurance and no motorcycle driver's license- operating a motorcycle like the OP's on a public road with no motorcycle endorsement, even if you have a valid car driver's license, is driving without a valid license, and is an arrestable criminal offense everywhere I've ever lived or worked as a cop. No insurance company is gonna issue insurance on something like that, and no motorcycle insurance will get you a court date at the least, and is an arrestable offense in some jurisdictions.
I have significant professional experience in this area- when I post something, it's not just to take up space on the internet. Either way, this is like "the information buffet"- the reader is free to benefit from my wise counsel, and he is also free to disregard it at his peril...