Shares of Apple jumped just over 5 percent in aftermarket trading immediately following the company’s hotly-debated, highly-anticipated fiscal third-quarter earnings report. The picture that emerged wasn’t all great but it did seem to soothe investors for the time being. 

Apple reported selling 31.2 million iPhones, a record for the June quarter, compared to 26 million in the same quarter last year. iPad sales hit 14.6 million during the quarter, compared to 17 million last year. 

Apple did not break out sales by model, but CFO Peter Oppenheimer said in a conference call that iPhone 5 remains “by far the most popular iPhone,” adding that the company was “very pleased” with sales of iPhone 4 and iPhone 4S. 

Piper Jafray analyst, Gene Munster, expected strong iPhone sales in the United States to offset declines in international sales. He had expected sales of iPhones to remain flat year over year at 26 million, with iPad sales totaling 18 million.

Quarterly revenue hit $35.3 billion while net profits were $6.9 billion, or $7.47 per diluted share. That compares to revenue of $35 billion and net profit of $8.8 billion, or $9.32 per diluted share, in the year-ago quarter.

Gross margins fell in line with analyst expectations of 36.5 percent compared to 42.8 percent in the year-ago quarter. 

International sales accounted for 57 percent of the quarter’s revenue.

Many watching Tuesday’s earnings were looking for assurances that Apple could pull out of the dive it has endured lately. The company’s stock, which the late Steve Jobs panned as out of the company’s control, has had a rough go of it lately, Apple’s 52-week range founds its ceiling back in October of 2012 at $705, and its bottom at $385 in April of this year. Investor worries have hinged on everything from supply problems to a lack of innovation in a competitive devices market. 

Apple is provided fourth-quarter guidance revenue between $34 billion and $37 billion, with gross margins between 36 percent and 37 percent. Operating expenses are expected to be between $3.9 billion and $3.95 billion. 

Oppenheimer said Apple is “on track” to have a very busy fall. The company is readying for the launch of its rebuilt mobile operating iOS 7. Historically, the launch of a new version of iOS will mean new devices. 

Apple CEO Tim Cook said he’s optimistic about the companies opportunities for growth, saying the company could expand everything from its retail outlets to its product lines, both in categories it currently works in and in others. 

On the matter of sticking with high-end products, particularly smartphones, Cook said he feels that there’s still room for growth in the space. 

“I don’t subscribe to the common view that the high-end smartphone market is at its peak,” Cook said.

When talking about the iPad, Cook referenced reports on Web share, which showed that 84 percent of all web traffic from tablets came from iPads.  

“If there are lots of other tablets selling, I don’t know what they’re being used for,” Cook said. 

Shares of Apple had settled to around $435 or an aftermarket gain of around 4 percent by the end of Tuesday’s call.