For "intensely" or "with great energy":
* Calmly
* Leisurely
* Slowly
* Tranquilly
* Deliberately
* Methodically
For "excitedly" or "with great eagerness":
* Indifferently
* Apathetically
* Dispassionately
* Calmly
* Reluctantly
For "urgently" or "with haste":
* Slowly
* Patiently
* Calmly
* Deliberately
For "frantically" or "with agitation":
* Calmly
* Peacefully
* Serenely
* Composedly
The best antonym will depend on the specific situation.