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Replace Calculator with PCalc
If all you expect from your calculator is a bit of adding and subtracting, then the built-in Calculator app is fine, but if you want a little more you need PCalc Lite.
PCalc Lite gives you all the power of a scientific calculator on your iPhone or iPad, including unit conversions and constants. If you want more features -- such as multi-line, engineering features, or programmer features -- they can be purchased separately.
Image source: TLA Systems.
Replace Camera with Camera+
I've taken more photos with my iPhone than any other camera I've ever owned. While I find the default Camera app to be acceptable, there's one app that can transform the iPhone -- or iPad -- from good camera into a great camera.
My favorite app is Camera+. Along with being able to activate the camera shutter, Camera+ has the following features:
- Quality settings allow you to take high, medium and low quality photos based on your need;
- Continuous flash;
- Advanced shooting modes, including burst and timer;
- Filters and effects.
Image source: Tap Tap Tap.
Replace Photos with Exif Wizard
The default Photos app annoys me for a number of reasons. Specifically, I can't understand why the app doesn't show me the date or time when a picture was taken, and refuses to give me access to the EXIF information stored with the photograph which contains detailed information relating to the photo.
The best app for this purpose is Exif Wizard. This can access photos from your photo rolls and show you all the hidden data saved along with the image.
If you want more features -- such as the ability to access photos stored on iCloud or work servers with images up to 13 megapixels in resolution -- you can upgrade to the Pro version for $1.99.
Image source: homedatasheet.com.