Earlier, ninth seed Gaston Gaudio became the first big name to fall in the men's draw.
The last semi-final spot will be decided on Friday when Gaston Gaudio plays Fernando Gonzalez.
Fellow Argentine and fourth seed Gaston Gaudio beat Germany's Lars Burgsmuller 4-6 6-2 6-4.
Gaudio awaits the winner of Wednesday's second quarter-final between fellow Argentine David Nalbandian and Brazil's Gustavo Kuerten.
" But a presidential swap, says the park's Ms. Gaudio, would be too much of "a political challenge.
Gaudio has already reached the semi-finals of three tournaments this season at Vina del Mar, Buenos Aires and Hamburg.
Gaudio, in his first major quarter-final, never lost his grip on the match and earned five more service breaks.
"I was expecting to make a better tournament here, but I played a guy that today was better than me, " admitted Gaudio.
Argentina, who thrashed Germany 5-0 in the first round, have David Nalbandian, Gaston Gaudio, Mariano Zabaleto and Lucas Arnold in their team.
Gaudio taught his seeded opponent a lesson in claycourt tennis, using acute angles to send the Australian scurrying all over Chatrier Court.
"It has always been my dream to win this tournament, " said Gaudio.
The Tennessee native announced his arrival on the senior circuit with a win over ninth seed Gaston Gaudio at the 2005 U.S. Open.
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The editor then suggested that, if any money were to change hands, it should be Gaudio who paid for the improvements made to her copy.
"On-field data tracking is one of the most important elements coaches and trainers use to prepare their teams, " said Paul Gaudio, vice president of adidas interactive.
Safin, who won the title in Barcelona in 2000, will face the winner of the match between defending champion Gaston Gaudio of Argentina and Spain's David Sanchez.
Seventh seed Gaston Gaudio of Argentina edged past France's Cyril Saulnier, while American veteran Agassi, the eighth seed, was a 6-4 4-6 6-2 winner over countryman Paul Goldstein.
The writer, Monica Gaudio, was alerted by a friend that her piece on the origins of apple pie, written for a website on medieval recipes, had been reprinted, sans permission, in Cooks Source, a small-scale publication based in New England.
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