I am a native Spanish speaker and "I may" would be translated, for example in the sentence "i may be able to do it" "puede que sea capaz de hacerlo" or even a bit more hard to understand (and a bit reiterative, but still working) "puede que pueda hacerlo". So, in this Duolingo is okay. it is the same verb, true, but different verbal tense.
"I am able" would be "Soy habil" or "Soy capaz" and is a verb and an adjective, with a different meaning, along the lines of "I am handy." Poder means "I can" or "I am able to" and usually relates to a specific task. "Poder" is often followed by another infinitive, like "hacer" "Puedo hacerlo" = I can do it.
Because In English the infinitive is given by 'to' the Spanish infinitives are: AR- ER- IR- When you translate into Spanish ‘I am able work’ you will say: ‘Yo puedo trabajo’ and what you want to say is: I am able to work. Translation: “Yo puedo trabajar”
I hope this will help.