Dishwasher hose to 1/2" (5/8 OD)?

My old dishwasher was connected to the hot water line with copper pipe and compression fittings. I don't know how that was attached to the intake on the dishwasher because the delivery people took the old one away. :-(

Now my problem is that a standard dishwasher hose will not connect to the valve on the hot water line, and the old copper tubing that will connect to the hot water line will not connect to the dishwasher. I've tried to find an adaptor, or combination of adaptors, to make the connection but have had no luck. By carrying my old piece of copper tubing around a hardware store and seeing what the compression nuts would connect to, I think the valve on the hot water line is 1/2" (5/8 OD).

Advice?

What is the out let side of the valve? Is it a flare fitting (sort of bulges out), or compression (pipe slips inside a bit)?

Compression, if I'm understanding the terminology correctly. The prior hookup was by copper tubing that slipped inside this outlet and was tightened by a nut against a little ring slipped around the tubing. So I'm trying to bridge the gap somehow between a shutoff valve designed to work that way, and a standard dishwasher hose which clearly operates on a completely different paradigm.

Of course I'm sure I could just replace the shutoff valve with something designed to work with a modern dishwasher hose, but at that point I think I have to give up on DIY...