To solve the given optimization problem, let's first break down the natural language description into a symbolic representation. This will help in understanding and translating the problem into Gurobi code.

The variables can be represented as follows:
- Let \(x_1\) represent the number of algebra questions answered.
- Let \(x_2\) represent the number of calculus questions answered.

Given this, the objective function (to maximize the score) can be written as:
\[ \text{Maximize: } x_1 + 3x_2 \]

The constraints based on the problem description are:
1. The total number of questions answered cannot exceed 25: \(x_1 + x_2 \leq 25\)
2. At least 10 algebra questions must be answered: \(x_1 \geq 10\)
3. At least 6 calculus questions must be answered: \(x_2 \geq 6\)
4. No more than 15 questions of either type can be answered: \(x_1 \leq 15\) and \(x_2 \leq 15\)

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'number of algebra questions'), ('x2', 'number of calculus questions')],
    'objective_function': 'x1 + 3*x2',
    'constraints': ['x1 + x2 <= 25', 'x1 >= 10', 'x2 >= 6', 'x1 <= 15', 'x2 <= 15']
}
```

To solve this problem using Gurobi in Python, we will use the following code:
```python
from gurobipy import *

# Create a new model
m = Model("Math_Contest")

# Add variables
x1 = m.addVar(lb=10, ub=15, vtype=GRB.INTEGER, name="algebra_questions")
x2 = m.addVar(lb=6, ub=15, vtype=GRB.INTEGER, name="calculus_questions")

# Set the objective function
m.setObjective(x1 + 3*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 25, "total_questions")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Algebra questions: {x1.x}")
    print(f"Calculus questions: {x2.x}")
    print(f"Maximum score: {m.objVal}")
else:
    print("No optimal solution found")
```