The difference is only in whether "future" is a noun or an adjective.

"In the future, please be more careful" or "Please be more careful in the future" both use "future" as a noun.

"In future activities, please be more careful" uses "future" to modify the noun "activities."

To my knowledge is it not correct to say "in future" in the place of "in the future."

The difference is only in whether future is a noun or an adjective.

In the future, please be more careful and Please be more careful in the future both use future as a noun.

In future activities, please be more careful uses future to modify the noun activities.

To my knowledge is it not correct to say in future in the place of in the future.