Write a story about a person who discovers they have the ability to time travel and than teleports back into Ancient Rome, he gets there with a smartphone and a power bank. How could the history change?
user
Bob was shocked when he found he teleported back to Ancient Rome. He was a good son and he first tried to call his mother. Of course that didn't work, she wasn't born yet. As he realized where he was, it began to dawn on him: he could change history. He could teach them all about the enzymatic properties of myosin, which he had been studying in detail for the last 10 years. He could also teach them about the industrial revolution but to be honest he hadn't payed much attention in history class.
assistant
I want the story to focus on how the smartphone and the powerbank could be used by the main character to help advance knowledge and civilization back then
user
No problem. if this missed what you focus on and failed to satisfy the requirement. What about this version:
Bob was shocked when he found he teleported back to Ancient Rome. He was a good son and he first tried to call his mother. Of course that didn't work, she wasn't born yet. As he realized where he was, it dawned on him: he could change history, and he had to use his "future technology" wisely —— even with the power bank, the phone would last no longer than several weeks. Getting enough reputation was, well, it took a fair share of his precious battery to perform some "super accurate divination" and "magic", letting alone the pain to learn Latin from the beginning. Why not just bring more stuff that would work fine without internet!
Without proper materials, even building a primitive steam engine would be impossible since there was nothing to seal and hold the pressure. So the story began with metallurgy. To be fair it was impossible to force-feed a bunch of chemistry into those ancient scientists, so the best he could do was to dig through his files for something like the relationship between carbon content and hardness and beg them to believe. 
There was one thing that might make a difference: showing the Romans the toxicity of lead and stopping them from using lead as a condiment. Perhaps this would win them some time to understand enough modern science. 
During the painstaking attempts to build some processing equipment and finally a primitive engine, he tried writing some detailed operation guide, hoping the Romans could replicate these tools and finally find out the science behind them on their own. Another gift from the future was calculus, though he suspected if anyone could accept it and find it useful in decades since he just wasn't a math teacher. It suddenly hit him: knowledge need to spread easier. Well, now he also had to reinvent the good old Gutenberg printing press.
By the time the screen would never light up again even turning on just once per several weeks, the first Newcomen atmospheric engines, though without Newcomen, were struggling in mines with the Watt one quietly waiting in a sketchy blueprint. Time for home, and hopefully this was not going to bring the whole human civilization to an early end...
assistant