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Trader Richard Scardino works on the floor of the New York Stock Exchange on Monday. Wall Street posted another solid gain as some of the gloom over the European debt crisis lessened.

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NEW YORK — What bear market?

Stocks surged on the latest positive news out of Europe on Monday, the fourth sharp increase in the last five days. It’s a dramatic turnaround from last Tuesday, when the S&P 500 index nearly fell enough to meet the definition of a bear market. Since then the widely used index has soared 8.7 percent.

Indexes soared in the U.S. and Europe after French and German leaders promised to strengthen European banks.

German Chancellor Angela Merkel and French President Nicolas Sarkozy said they would finalize a “comprehensive response” to the debt crisis by the end of the month, including a plan to make sure European banks have adequate capital. Investors have been worried that European leaders weren’t moving quickly enough to contain the fallout from a default by Greece’s government.

“The more we can put our arms around the problem with a little more detail, the better, and time frames usually help,” said Michael Sansoterra, a portfolio manager at Silvant Capital Management in Atlanta.

Investors have been worried that a default by Greece could cause the value of Greek bonds held by those banks to plunge, hurting their balance sheets. U.S. banks could also be affected if Greece goes through a messy default, since they own Greek bonds and also have close ties to European banks.

Apple Inc. rose 5.1 percent to $388.81 after reporting that first-day orders for its new iPhone topped 1 million. Alcoa Inc. will become the first major U.S. company to report third-quarter results after the closing bell Tuesday. The aluminum maker’s stock rose 3.9 percent to $10.09. Bond trading was closed for the Columbus Day holiday.

Ten stocks rose for every one that fell on the New York Stock Exchange. Trading volume was light at 3.8 billion.