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Kaufmann,
If the flower is yellow with a red throat or a red base, then it is definately Not Opuntia engelmannii v. lindheimeri. Which has full deep orange-red flowers, like in this photo here: http://davesgarden.com/pf/showimage/125294/
This photo is either Opuntia santa-rita Or, Opuntia macrorhiza Or, Opuntia macrocentra, because it has the red base to the petals... I'd have to see the spines and pad to tell which it is. If I had to ascertain which one you have pictured here, I would probably say it's Opuntia macrorhiza. Do you have any photos of the pads or whole plant?
It has been suggested that the plant in your image is a different plant than Opuntia lindheimeri based on bloom color. If you are able to review the suggested ID's mentioned above and let us know which entry it should be moved to. Respond to this thread and we will move the image.