Assuming it has a full battery would a smart phone and some of its apps work on an alien planet? The environment on the planet is similar but not the same as Earth. In other words a human couldn't breath without equipment, but there are no significant differences in pressure. Would apps like a calendar, downloaded music, downloaded games work?
Yes. A modern smart phone will work fine in a non breathable atmosphere, from vacuum to about double Earth pressure. Anything that doesn't need an internet connection or GPS will work.
eg Samsung S9 is IP68. This means 8 hours of 1atm pressure difference no dust can get in, and 1.5m of water none gets in over half an hour.
If the atmosphere is corrosive, the phone will corrode, but itll take a long time to loose functionality. Smears on the screen and metallic paint on the back dripping off will be the first signs.
Note that the touch screen may not work through a space suits gloves. You may need to enable the extra sensitive touch screen function before you get there.
In a vacuum it will eventually overheat. It will slow down and turn off rather than be permanently damaged. You wont be able to fast charge it in a vacuum either (unless you rest the phone on a big solid cold thing to stop the waste heat pulling the Li Ion battery above the critical 45 degree max temperature.). A very slow charge may work.
Microphone and speakers obviously wont work in a vacuum. Sounds may be slightly distorted in a different atmosphere to earth but should be recognisable as the original.
Many apps that allow downloaded content will auto-lock after a period without an internet connection. Eg Amazon Prime will block downloads after 48 hours offline.
Edit: Apparently helium can turn a cpu oscillator off. I didnt know that, but that would be something to watch out for. Not a lot of helium at ground level on many nearby planets, and most modern phones are watertight, but still a risk of tiny helium getting in.
It would likely generally work, with the obvious exception that it would not have connectivity. There would be a few caveats.
Some phones, particularly iPhones, use a MEMS oscillator to run the processor. This depends on the atmosphere. Notably, a helium atmosphere prevents them from running, but does not damage them permanently. This can even happen on Earth if there is a helium leak, such as in this hospital.
High temperatures, even if not high enough to permanently damage the phone, may cause it to shut down. This can happen on earth if you have a phone mount in front of a heater vent. Similar situations may happen in vacuum or very thin atmospheres if the phone is not able to cool itself from the heat it produces.
Finally, vacuum may cause components in the phone to release gasses that don't form in an atmosphere. I'm not familiar with the effects, but I would expect it to cause weakening of adhesives (screen falling off) or fogging of the screen or camera.
In conclusion, there are a lot of possible issues, but it is not unreasonable for a modern smartphone to function outside of Earth's atmosphere.
We have sent probes to orbit other planets of our solar system, and in some cases they have even landed on their surfaces.
The most famous cases are probably the probes which have moved on the surface of Mars, like for example Curiosity.
Considering the sheer amount of information they have managed to send to us thanks to even simpler electronic than what we have today in a smartphone, I am sure apps which do not require connection to the internet would work fine.