Using Entity Framework Code-first am I required to have the model of my domain anemic?

Question

with Entity Framework Code-First I have to have all properties public to generate database, this mean using Entity Framework Code-First approach I am forced to have an anemic domain mixed with a rich model? Because Properties that need not be public, have to be.

For example:

Using a rich model, this in Entity Framework will not work:

public class Car
{
    private int _actualPosition;

    public void Accelerate()
    {
        this._actualPosition += 10;
    }
}

To work we need to make _actualPosition public:

public class Car
{
    public int ActualPosition { get; set; }

    public void Accelerate()
    {
        this.ActualPosition += 10;
    }
}

Now Entity IMO is ugly, because I have a method that adds + 10 in the property and have it public at the same time, I don't want that property be public.

Another Example:

Imagine I want a relationship many-to-many but with only one way like:

public class User
{
   public long Id { get; set; }

   public string Name { get; set; }

   public IList<Role> Roles { get; set; }
}

public class Role
{
   public long Id { get; set; }

   public string Name { get; set; }
}

How I do a many-to-many relationship with that model? To my knowledge there's no way I'll have to do a two-way relationship:

public class User
{
   public long Id { get; set; }

   public string Name { get; set; }

   public IList<Role> Roles { get; set; }
}

public class Role
{
   public long Id { get; set; }

   public string Name { get; set; }

   public IList<User> Users { get; set; }
}

With this model I'll be able to make many-to-many relationship:

modelBuilder.Entity<User>()
                .HasMany(x => x.Roles)
                .WithMany(y => y.Users);

I'm right? If yes, Entity Framework is not pleasing me.

The "Another Example" work with answer of @Slauma:

modelBuilder.Entity<User>()
            .HasMany(x => x.Roles)
            .WithMany()
            .Map(a =>
            {
                a.MapLeftKey("UserId");
                a.MapRightKey("RoleId");
                a.ToTable("UserRoles");
            });

Answer 1

Your "Another example" is not correct. You are not forced to expose both ends of a relationship as properties in your model classes. In your example you can remove public IList<User> Users { get; set; } from your Role class and define the mapping like so:

modelBuilder.Entity<User>()
            .HasMany(x => x.Roles)
            .WithMany()
            .Map(a =>
            {
                a.MapLeftKey("UserId");
                a.MapRightKey("RoleId");
                a.ToTable("UserRoles");
            });

This is the case also for one-to-many relationships. There is always a parameterless With... overload, WithMany(), WithRequired(), WithOptional(), etc. to define mappings for relationships where not both ends are exposed in the model.