If you are unfamiliar with A Certain Magical Index, the series has many adaptations of the original light novel. A Certain Magical Index currently has two television seasons and a full-length anime film. In addition, the series has a spin-off manga, A Certain Scientific Railgun, which has inspired an OVA and two animated adaptation TV series’.
You can see the description of the film from Crunchyroll :
"Kamijo is a student in Academy City, where people use science to develop supernatural abilities. The guy’s got a lot of heart – luckily for a young nun named Index. She’s on the run from a sorcery society that covets the astonishing 103,000 volumes of magical knowledge stored in her memory. When Index stumbles into Kamijo’s life, she finds a faithful friend and protector, and while Kamijo’s easily the weakest kid in Academy City, he’s got something else going for him: the Imagine Breaker, an unexplainable power stored in his right hand that negates the powers of others."
The film is about Kamijo, nun-in training index, and some of their allies, as well as some former enemies, attempt to protect a beautiful and talented singer. This singer is somehow linked to their futuristic city’s sky-piercing space elevator, which means she is of great importance.
Meanwhile, as for Eureka Seven, its original animated series ran for 50 episodes and Bandai Visual has given fans its description of the series.
"Ten years ago, the major earth-shaking “First Summer of Love” event occurred. Renton, who lost his father during the event, now attends the army school of the United Federation of Predgio Towers located in the border town of Bellforest. Because his late father is still praised, Renton feels something is lacking as he continues with his ordinary, boring days. Then one day, Nirvash, the world's oldest LFO, appears in front of him and a girl named Eureka emerges from the cockpit. This was the beginning of the future of humans and Scub Coral, another intelligent lifeform.Was this encounter all just a coincidence? Or was it fate? Where will Renton and Eureka's journey end?"
Whilst the film will showcase an alternate timeline, with mankind preparing to fire a weapon that will end a half-century war. The worlds fate rests in the hearts of two recently reunited childhood friends and so the film follows their story. Both films have now been officially released for streaming on Crunchyroll for all anime fans to enjoy.