Apple does not offer and will not perform any data recovery service.
A simple google search will reveal multiple data recovery services, if you really need such a service and are willing to pay an arm, a leg, and give up your first born child for that data.
If the device has been used as designed, it would have been backed up regularly to iTunes or iCloud.
Simply restore that backup to a new iOS device.
Contacts and calendars should be synced to a supported application on the computer or a cloud service.
Pictures taken with the device should be regularly copied off the device to a computer as would be done with any digital camera.