Your task is to define a function that understands basic mathematical expressions and solves them.
For example:

```python
calculate("1 + 1")        # => 2
calculate("18 + 4*6")     # => 42
calculate("245 - 826")    # => -581
calculate("09 + 000482")  # => 491
calculate("8 / 4 + 6")    # => 8
calculate("5 + 1 / 5")    # => 5.2
calculate("1+2+3")        # => 6
calculate("9 /3 + 12/ 6") # => 5
```
Notes:

- Input string will contain numbers (may be integers and floats) and arithmetic operations.
- Input string may contain spaces, and all space characters should be ignored.
- Operations that will be used: addition (+), subtraction (-), multiplication (*), and division (/)
- Operations must be done in the order of operations: First multiplication and division, then addition and subtraction.
- In this kata, input expression will not have negative numbers. (ex: "-4 + 5")
- If output is an integer, return as integer. Else return as float.
- If input string is empty, contains letters, has a wrong syntax, contains division by zero or is not a string, return False.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "import math\ndef solve(s: list, mp=0):\n    LHS = s.pop(0)\n    while len(s) > 0:\n        #\n        op = s[0]\n        #\n        p = 1 if op in '+-' else 2\n        if p < mp: break\n        p += 1\n        s.pop(0)  #drop the operator because it being used\n        #\n        RHS = solve(s, p)\n        if   op == '+': LHS+=RHS\n        elif op == '-': LHS-=RHS\n        elif op == '*': LHS*=RHS\n        elif RHS  != 0: LHS/=RHS\n        else:           return math.nan\n    return LHS\n\ndef calculate(s):\n    try:\n        s=s.replace(' ', '')\n    except:\n        return False\n    #\n    dim = len(s)\n    #\n    if dim == 0: return False\n    #\n    for c in s: \n        if not (c in '0123456789.+-*/'): return False\n    for i in range(dim-1):\n        if s[i] in '+-*/' and s[i+1] in '+-*/': return False\n    #\n    exp = []\n    i=0\n    for j,c in enumerate(s):\n        if i==j:\n            pass\n        elif c in ['+','-','*','/']:\n            try:\n                exp.append(float(s[i:j]))\n            except:\n                return False\n            exp.append(s[j])\n            i=j+1\n    try:\n        exp.append(float(s[i:]))\n    except:\n        return False\n    #\n    v = solve(exp)\n    #\n    if math.isnan(v):             return False\n    if float(v) == float(int(v)): return int(v)\n    return v"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'calculate'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6524