AirfareWatchdog shows some $600+ round-trip fares from Miami to Berlin and Rome. This is for travel next month and May.
Book on the AirBerlin website.
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airberlin – $644: Miami – Rome, Italy. Roundtrip, including all Taxes
AirBerlin is a OneWorld partner, so you can earn American AAdvantage miles on these flights if you ask in advance of travel.