Oops, I thought you were trying to ID the plant.
Yes, I know about them. It's a love/hate relationship.
Mostly love though.
These are a couple of my Opuntia humifusa(s). Several are rooting on the ground. I can't find a photo of their blooms right now, but it's a yellow flower similar to the flower in your top picture. Large flower and large pads.
I have other Opuntias as well.