Phrasal Verb: Come

to come up with s.t.- to think of an idea, answer etc: 
"Can you come up with an idea for the party theme?" 
"Steve Jobs came up with the Iphone" 
"I've been working on this math problem for ages. I can't come up with the answer." 

to come down with s.t. - to get an illness
"I've come down with a cold"
"Last week, she came down with a terrible cough."

"Come On!" (spoken)
1. to get s.o to hurry
"Come on, we're going to be late! Move it!"
                                                        2. to encourage s.o.
                                                      "Come on, you can do it! Keep going!"
                                                       3. to express disbelief
                                                       "Come on, you're kidding right? You must be lying."

To be coming up-  to be happening soon
"Coming up next, breaking celebrity news!"
"My birthday is coming up really soon!"
"My final exam is coming up next week, better start cramming..."

To come up
1. sun/moon - to rise
"The sun came up at 6:03 this morning."

2. subject/topic of disuccsion (s.o. mentions it and discusses it)- to arise
"This week in class, the subject of culture shock came up when we were talking about travel"
"Politics always comes up during their conversations over coffee."

3- Problems/difficulty- to arise
"Sorry, I can't go out tonight, something has come up. "
"During grammar tests, the same problems come up everytime."

To come back
1-to return to a particular place (that you are currently in/at) *vs. to go back
Leaving Vancouver: "I really want to come back to Vancouver one day!"

2-to become popular/trendy/fashionable again  (to make a comeback)
"Boyband music has been making a comeback in 2012."
 "Skinny jeans are coming back into fashion"