I wouldn't back away, espcially if it looked like it was stalking me, but in the very unlikely possibility that is was a female with cubs I would back away. I lived in cougar country (Washington State) for 20 years, hiked, fished, and hunted quite a bit and never saw one. But I had a game plan on what to do if I ran into one. And if I was going to slowly back away, and I wouldn't unless cubs were present, I would not be quiet about it, the cougar knows you are there, let it know you know it's there. But that's me, you can decide on what you're going to do if you bump into one. And if you're backing away, be sure of your footage, it's not a good time to trip and fall when a predator is stalking you.