Naming
Java classes start with a capital letter and do not use underscores, so rock_paper should be RockPaper. Java uses camelCase, not snake_case, for all variable names except constants (static finals), so user_choice should be userChoice.
Spacing
The convention in java is to include whitespace before and after operators such as +, =, != or ==, so count_win=0 should be countWin = 0. Curly braces should be on the same line as an if or else.
Variable Declarations
You declare a new Random() inside your loop, so you might wind up making 19 Random objects, when you only need one. Declare it outside the loop. Conversely, you declare user_choice and computer_choice outside the loop, but they're only used inside. They should have the smallest possible scope.
Branching
You're branching (using if conditional statements) a lot to look up the name of a numeric selection. If you've learned about arrays, you could use a String[] of choices to simplify that lookup. There are a ton more branches to determine who wins. You only need one comparison to determine if there's a tie, and then only three specific checks to see if the user wins. Otherwise, the computer wins.
Making all those changes might look something like this:
import java.util.Random;import java.util.Scanner;public final class RockPaperScissors { private static final String[] CHOICES = { "rock", "paper", "scissors" }; public static void main(final String[] argv) { final Random random = new Random(); final Scanner keyboard = new Scanner(System.in); int computerWins = 0; int userWins = 0; System.out.println("\n Let us play Rock Paper Scissors \n"); while (computerWins <= 10 && userWins <= 10) { /* Read user input and determine choice */ System.out.println("\n Enter your choice 0 for rock, 1 for paper, or 2 for scissors \n"); final int userChoice = keyboard.nextInt(); if (userChoice < 0 || userChoice > 2) { System.out.println("Incorrect choice"); continue; } else { System.out.println("\n Your choice was \n" + CHOICES[userChoice]); } /* Randomly generate computer input */ final int computerChoice = random.nextInt(3) + 1; System.out.println("\n The computer choice was \n" + CHOICES[computerChoice]); if (userChoice == computerChoice) { System.out.println("Tie"); continue; } if (userChoice == 0 && computerChoice == 1 || userChoice == 1 && computerChoice == 2 || userChoice == 2 && computerChoice == 0) { System.out.println("\nThe user wins!"); userWins++; } else { System.out.println("\nThe computer wins!"); computerWins++; } } }}Review Note: I intentionally don't close the Scanner because I'm assuming that hasn't been covered yet.
