Federer's opponent on Friday will be the winner of the quarterfinal late Thursday between No. 1 Rafael Nadal and No. 7 Tomas Berdych.
Federer beat Nadal for the Key Biscayne title early in their rivalry in 2005, and they haven't played each other in the United States since.
The No. 3-seeded Federer won 12 of the 15 points on Thursday against Simon, and the match lasted only 10 minutes. Simon talked with a trainer during the changeover before conceding by shaking hands with Federer.
Simon then walked off the court to boos from the stadium crowd.
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