May I ask: what does it stand for?
I got you an addy with a number after the prefix. This way it stands out a bit more:
Address: 1qHKG5xn7H3iDfgb1LYQ69quacMqnqBjw (Balance: )
PrivkeyPart: 5J11srdr67BQGCLPHYGWK1cw6CXzDkjYYdvxTYyAMgW6mhTzTqJ

How much would it cost for the prefix 1DarkStr generated as a compressed (-F compressed command in Lifeboat) address?

My current vanity isn't compressed, so I'd be interested to see how much it would cost so I can calculate whether it would be worth it for me to save on fees, in the long run. Alternatively, just to lower the difficulty (and cost) by a little bit, how about whichever of these comes first:

Let me try this.

Prefix desired: iLoveU
Public key: 04D3D711DEB706681D9F469B5A4B1D973AE6379F1AF2313CBF47EC464C71A8B85271E7C140CA757 67E0ED0C4E232E1AF91EC85F2996B8497B4F0AACB5EEB54D207

I will take the 1LoveU, thank you 

It would cost you an infinite sum of bitcoins, as the address 1MintCtNesdc8EiJ2D1sKs75EUYPABD3LX has an invalid checksum, meaning it can never be a valid bitcoin address. There is no private key that belongs to that address.

Even if it is an valid address, it's almost impossible to vanitygen an entire address, as the chance is extremely extremely extremely extremely extremely extremely low to find an exact match. Why do you even want to random string of characters (I assume)?

You can get 1Mint for free, if that's all you want. I can do it right now for you or you can wait for Loyce to come online.

True, the complications may well make it less efficient for this give-away, but I think it would be beneficial to have a program that does this.
Also, I cannot imagine parting with half a bitcoin just to get a fancy address.

Edit:
Public key: 04AAE1C6D854E3F1D1AB271D76D2BF1E09912C8B278766F9F6AB41FF6F38576D950C71F820700DA 77B9F659391377F263D92A4F42C38B32FF9E6F33369B0EBD6DC

sorry for inconvenience sir

Thank you very much sir LoyceV! Keep up the good work by helping the community. Kudos!

Not quite, for a normal bitcoin address, while the coins are stored on it only the hash of the public key is public, and the public key itself is only revealed when the coins are spent.
With a vanity address, the public key is made public as soon as the address is generated.
The hash is practically intractable, but ECDSA can be easily cracked using a quantum computer, and may possibly be susceptible to mathematical analysis.
Vanity addresses give more time for such attacks than ordinary addresses.
Since practical quantum computers don't exist yet (or perhaps "the powers that be" have one in the basement, but don't use it for fear of revealing its existence, an interesting conspiracy theory), and no mathematical attacks are known, vanity addresses are probably safe.
Only if they use the same address algorithm as bitcoin, be very careful, as if the altcoin uses the same format but a different algorithm, the coins would be burned.