3,000mAh+ Phone? Look no further than Qmobile Power 1000! It's a small 'bar phone' with a HUGE 4,000mAh battery! Can easily last you A MONTH on stand-by! I might buy one...
Android Smartphones? Qmobile M Series usually have big batteries as M stands for... Duh... Marathon!
M95 has 4,000mAh, while M300 has a HUGE 5,000mAh! Then there's Lenovo 5000 which, quite ironically, has 4,000mAh battery instead of suggesting 5,000mAh.
There might be few more though... But you won't find any smartphone with battery bigger than 4,000 except M300...
Alternatively, consider Lumia Phones. A 1,500mAh Lumia 435 can easily out-last an Android with 2,500mAh to 3,000mAh battery! But I'm hearing that latest Android Marshmallow is 50% more power efficient than Kitkat!
Guess we'll soon find out!